Topological Solitons

DOI10.1017/CBO9780511617034zbMath1100.37044OpenAlexW4214625835MaRDI QIDQ4821315

Sutcliffe, Paul M., Nicholas S. Manton

Publication date: 12 October 2004

Full work available at URL: https://doi.org/10.1017/cbo9780511617034

instantons solitons vortices kinks skyrmions topological solitons sphalerons Dirac monopoles

Symplectic and contact topology in high or arbitrary dimension (57R17) Yang-Mills and other gauge theories in quantum field theory (81T13) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Topology of vector bundles and fiber bundles (57R22) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02)

Related Items

Noise-induced kink propagation in shallow granular layers, Chaotic solitons in driven sine-Gordon model, Faster-than-light solitons in $1+1$ dimensions, An asymptotic expansion of two-bubble wave maps in high equivariance classes, New class of solutions in the non-minimal O(3)-sigma model, Parabolic Higgs bundles and cyclic monopole chains, Holographic coordinates, Cartan connections and integrable vortex equations, Novel results for kinklike structures and their connections to quantum mechanics, First order formalism for generalized vortices, Magnetic skyrmions at critical coupling, Symmetry reductions of the Skyrme-Faddeev model, BPS center vortices in nonrelativistic $S U(N)$ gauge models with adjoint Higgs fields, The attenuated ray transform for connections and Higgs fields, Strolling along gravitational vacua, Boundary charges and integral identities for solitons in $(d+1)$-dimensional field theories, Magneto-dimensional resonance. Pseudospin phase and hidden quantum number, Asymptotic stability of large energy harmonic maps under the wave map from 2D hyperbolic spaces to 2D hyperbolic spaces, First singular homology group of spacetime, Dynamics of monopole walls, Multi-kink collisions in the ${\phi}^{6}$ model, Exact self-duality in a modified Skyrme model, Kink dynamics in a system of two coupled scalar fields in two space-time dimensions, Kinklike structures in models of the Dirac-Born-Infeld type, Scattering of the $\varphi^8$ kinks with power-law asymptotics, Finite-action solutions of Yang-Mills equations on de Sitter $\mathrm{dS}_{4}$ and anti-de Sitter $\mathrm{AdS}_{4}$ spaces, Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension, Analytic vortex solutions in generalized models of the Maxwell-Higgs type, Kink dynamics in a parametric ${\phi}^6$ system: a model with controllably many internal modes, Interaction of Dirac $\delta$-waves in the nonlinear Klein-Gordon equation, Biadjoint wires, Kink-antikink collisions in the periodic $\varphi^4$ model, Stability catalyzer for a relativistic non-topological soliton solution, Non-Abelian global vortices, Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices, Quantum soliton scattering manifolds, A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree $\pm 1$ harmonic maps from $\mathbb{R}^2$ to $\mathbb{S}^2$, Spectral curves are transcendental, Stability of kinklike structures in generalized models, Gravitating solitons and black holes with synchronised hair in the four dimensional O(3) sigma-model, Resurgence in the bi-Yang-Baxter model, Kink properties in Lorentz-violating scalar field theory, Configurational entropy of skyrmions and half-skyrmions in planar magnetic elements, Interaction between kinks and antikinks with double long-range tails, Complex BPS skyrmions with real energy, Skyrme model from 6d $\mathcal{N} = (2, 0)$ theory, Spectral walls in multifield kink dynamics, BPS Skyrme submodels of the five-dimensional Skyrme model, Wobbling double sine-Gordon kinks, A low-energy limit of Yang-Mills theory on de Sitter space, Resonance structures in kink-antikink collisions in a deformed sine-Gordon model, A differential relation between the energy and electric charge of a dyon, Scattering of metastable lumps in a model with a false vacuum, Magnetic zero-modes, vortices and Cartan geometry, Kähler quantization of vortex moduli, Introducing a relativistic nonlinear field system with a single stable non-topological soliton solution in $1 + 1$ dimensions, Planar ringlike vortices, Some exact solutions for maximally symmetric topological defects in Anti de Sitter space, Skyrmions, instantons and holography, Self-duality in the context of the Skyrme model, On the curvature of vortex moduli spaces, Instantons on conical half-flat 6-manifolds, Dyonic non-abelian vortex strings in supersymmetric and non-supersymmetric theories -- tensions and higher derivative corrections, Yang-Mills instantons and dyons on homogeneous $G_{2}$-manifolds, Deformed Skyrme crystals, Exact vortex solutions in a $\mathbb{CP}^{N}$ Skyrme-Faddeev type model, High energy density in the collision of $N$ kinks in the $\phi^4$ model, The geometry of the space of BPS vortex-antivortex pairs, New results on compact structures, Vortices as degenerate metrics, Weyl equation and (non)-commutative $\mathrm{SU}(n + 1)$ BPS monopoles, On critical points of the $\sigma_2$-energy over a space of measure preserving maps, Skyrmion interactions and lattices in chiral magnets: analytical results, Bubble evolution around heterogeneities in $\varphi^4$-field theories, Twisted Hilbert spaces of 3d supersymmetric gauge theories, Chern-Simons deformation of vortices on compact domains, Large data global regularity for the classical equivariant Skyrme model, Soliton-like excitations in weakly dispersive media, The worldvolume action of kink solitons in AdS spacetime, Non-abelian self-dual string solutions, A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models, Non-abelian sigma models from Yang-Mills theory compactified on a circle, Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities, Magnetic impurities, integrable vortices and the Toda equation, On asymptotic stability of nonlinear waves, Dirac quantization and baryon intrinsic frequencies in hypersphere soliton model, On the efficient computation of large scale singular sums with applications to long-range forces in crystal lattices, Deformations of kink tails, Asymmetric scattering between kinks and wobblers, Fractional skyrmion molecules in a $\mathbb{C}P^{N- 1}$ model, Analytic multi-baryonic solutions in the $\mathrm{SU}(N)$-Skyrme model at finite density, Stable $Z$-strings with topological polarization in two Higgs doublet model, A detailed study of the stability of vortons, Electroweak monopoles and their stability, Scattering of fermions on a one-dimensional Q-ball, Instanton expansions and phase transitions, Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry, Vortex, stripe, Skyrmion lattice, and localized states in a spin-orbit coupled dipolar condensate, Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line, Ground state of the Frenkel-Kontorova model with a globally deformable substrate potential, On global singularities of Sobolev mappings, Parameter counting for singular monopoles on $\mathbb{R}^3$, Matter accretion onto higher-dimensional black holes with Dirac-Born-Infeld global defects via well known fluids, A cohomological approach to immersed submanifolds via integrable systems, Skyrmion states in chiral liquid crystals, Soliton solutions of the fermion-skyrmion system in (2+1) dimensions, Skyrmions around Kerr black holes and spinning BHs with Skyrme hair, False vacuum decay in kink scattering, Dimensional regularization approach to the renormalization group theory of the generalized sine-Gordon model, Magnetic monopoles in multivector boson theories, Skyrme-Faddeev model from 5d super-Yang-Mills, Magnetic monopoles in Lorentz-violating electrodynamics, Optical knots and contact geometry. I: From Arnol'd inequality to Ranada's dyons, Periodic monopoles from spectral curves, Extended supersymmetry and BPS solutions in baby skyrme models, ADHM polytopes, Non-abelian self-dual string and M2-M5 branes intersection in supergravity, Lie and Noether point symmetries of a class of quasilinear systems of second-order differential equations, Domain walls in a non-linear $ {\mathbb{S}}^2 $-sigma model with homogeneous quartic polynomial potential, Skyrmions from calorons, Vortex motion on surfaces of small curvature, Vortices with scalar condensates in two-component Ginzburg-Landau systems, The first-order Euler-Lagrange equations and some of their uses, Yang-Mills solutions and $\mathrm{Spin}(7)$-instantons on cylinders over coset spaces with $G_2$-structure, Scalar triplet on a domain wall: an exact solution, Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors, Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models, Semiclassical framed BPS states, How to build a compact brane, Classical dynamics of the abelian Higgs model from the critical point and beyond, Non-vortex topological solitons of the $\mathbb {CP}(1)$ gauge model, Solutions of the generic non-compact Weyl equation, Self-dual hopfions, Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem, The 6D superswirl, Multi-monopoles and magnetic bags, 1/2, 1/4 and 1/8 BPS equations in SUSY Yang-Mills-Higgs systems: field theoretical brane configurations, Nonintegrability of self-dual Yang-Mills-Higgs system, Spectral curves and the mass of hyperbolic monopoles, Vortices and the Abel-Jacobi map, The volume of the space of holomorphic maps from $S^{2}$ to $\mathbb C\mathbb P^k$, Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices, Ricci magnetic geodesic motion of vortices and lumps, Integrability of vortex equations on Riemann surfaces, Cosmology of the selfaccelerating third order Galileon, Existence of dyons in minimally gauged Skyrme model via constrained minimization, Supercharges, quantum states and angular momentum for N=4 supersymmetric monopoles, Relativistic dynamics of multi-BPS D-vortices and straight BPS D-strings, New models for two real scalar fields and their kink-like solutions, Cyclically deformed defects and topological mass constraints, On the $L^{2}$-metric of vortex moduli spaces, Lagrangian curves on spectral curves of monopoles, Non-Abelian sine-Gordon solitons, Scattering of Skyrmions, Statistical mechanics of vortices from D-branes and $T$-duality, A pure Skyrme instanton, Gauge and integrable theories in loop spaces, Low-energy vortex dynamics in the self-dual Chern-Simons-Higgs model, The concept of quasi-integrability: a concrete example, Discrete skyrmions in $2+1$ and $3+1$ dimensions, Solitons on tori and soliton crystals, Cyclic monopoles, affine Toda and spectral curves, Exact solutions of a fermion-soliton system in two dimensions, Monopoles in AdS, Classical behavior of deformed sine-gordon models, The little skyrmion: new dark matter for little Higgs models, One-loop kink mass shifts: A computational approach, A ladder of topologically non-trivial non-BPS states, $U(1) \times U(1)$ Chern-Simons solitons in background gravity, Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds, Self-dual sectors for scalar field theories in (1 + 1) dimensions, Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime, One-vortex moduli space and Ricci flow, Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics, Multikink solutions and deformed defects, Stable static structures in models with higher-order derivatives, On the geometrized Skyrme and Faddeev models, Adiabatic dynamics of instantons on $S^{4}$, Vortices and Jacobian varieties, Non-Abelian monopoles in the Higgs phase, On the non-existence of three-dimensional water waves with finite energy, Lorentz-violating effects on topological defects generated by two real scalar fields, Yang-Mills flows on nearly Kähler manifolds and $G_{2}$-instantons, Skyrmions in a truncated BPS theory, The non-compact Weyl equation, The generalized Fubini instanton, Construction of topological defect networks with complex scalar fields, On collapse of wave maps, On the formation of singularities in the critical $O(3)$ $\sigma $-model, Lump-like structures in scalar-field models in 1+1 dimensions, Instantons and Yang-Mills flows on coset spaces, BPS states for scalar field theories based on $\mathfrak{g}_2$ and $\mathfrak{su}(4)$ algebras, On the domain of moduli fields, Some decomposition method for analytic solving of certain nonlinear partial differential equations in physics with applications, Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schrödinger system, Instantons on Calabi-Yau cones, Yang-Mills solutions and dyons on cylinders over coset spaces with Sasakian structure, Vibrational quantisation of the $B=7$ skyrmion, On the range of the attenuated magnetic ray transform for connections and Higgs fields, A refined threshold theorem for $(1+2)$-dimensional wave maps into surfaces, Orbital stability and instability of periodic wave solutions for ϕ4n -models, Topology vs localization in synthetic dimensions, Dynamics of vortices with magnetic impurities, A model for gauged skyrmions with low binding energies, A mild source for the Wu–Yang magnetic monopole, On spacetime foliations and electromagnetic knots, Some comments on BPS systems, Quantum statistical mechanics of vortices, Family of potentials with power law kink tails, Exact instantons via worldline deformations, BPS Skyrme neutron stars in generalized gravity, Linear and orbital stability analysis for solitary-wave solutions of variable-coefficient scalar-field equations, Characteristic approach to the soliton resolution, Quadratic Klein-Gordon equations with a potential in one dimension, The existence of dyon solutions for generalized Weinberg–Salam model, Quantum statistical mechanics of dissolving Abelian Higgs vortices, Uniqueness of <scp>Two‐Bubble</scp> Wave Maps in High Equivariance Classes, Neumann boundary condition for abelian BPS vortices, Liquid Crystalline Half‐Skyrmions and Their Optical Properties, Towards a classification of charge-3 monopoles with symmetry, Composite topological solitons consisting of domain walls, strings, and monopoles in $O(N)$ models, Collective coordinate system in (2+1) dimensions: CP¹ lumps-potential interaction, The geometry of the space of vortices on a two-sphere in the Bradlow limit, Collisions of weakly-bound kinks in the Christ-Lee model, Sphaleron in the Higgs triplet model, Kink scattering in the presence of geometric constrictions, Periodic charge oscillations in the Proca theory, Noether symmetries and conservation laws of a reduced gauged bilayer graphene model, Hilbert series and higher-order Lagrangians for the $O(N)$ model, Dynamics of two interacting kinks for the $\phi^6$ model, Exact hopfion vortices in a 3D Heisenberg ferromagnet, Moduli space for kink collisions with moving center of mass, Spectral flow of vortex shape modes over the BPS 2-vortex moduli space, Pearcey integrals, Stokes lines and exact baryonic layers in the low energy limit of QCD, Kinks and branes in models with hyperbolic interactions, Geometrically constrained localized configurations: first-order framework and analytical solutions, Sharp universal rate for stable blow-up of corotational wave maps, Integration theory for kinks and sphalerons in one dimension, Magnetized baryonic layer and a novel BPS bound in the gauged-non-linear-sigma-model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation, Asymptotic stability of the sine-Gordon kink under odd perturbations, Multisoliton complex systems with explicit superpotential interactions, A nontopological soliton in an $\mathcal{N} = 1$ supersymmetric abelian gauge model, On the integrability and solitons of the $A_\pm$ equation, Kink-antikink collisions in the $\phi^8$ model: short-range to long-range journey, Solitons in the gauged Skyrme-Maxwell model, The asymptotic structure of the centred hyperbolic 2-monopole moduli space, Elizabethan vortices ^*, Rotationally invariant isospinning baby-skyrmions dressed by fermions, Q-lump scattering, When do knots in light stay knotted?, Properties of soliton surfaces associated with integrable $\mathbb{C}P^{N-1}$ sigma models, Bogomolny equations in certain generalized baby BPS Skyrme models, Hopf solitons on compact manifolds, Hereditary automorphic Lie algebras, Manton’s five vortex equations from self-duality, Unnamed Item, Hopfions, On a stack of surfaces obtained from the $\boldsymbol {\mathbb{C}P^{N-1}}$ sigma models, Existence of the topological solutions arising in vortices–antivortices equation, Non-abelian vortices on $\mathbb {CP}^{1}$CP1 and Grassmannians, A cosmological study of Einstein–Skyrme model in anisotropic Kantowski–Sachs spacetime using Lie and Noether symmetries, Skyrme fields, multi-instantons and the $SU(\infty)$ -Toda equation, Platonic solids generate their four-dimensional analogues, Twistor theory at fifty: from contour integrals to twistor strings, NON-ABELIAN VORTEX-STRING DYNAMICS FROM NONLINEAR REALIZATION, An unconstrained Lagrangian formulation and conservation laws for the Schrödinger map system, From scalar field theories to supersymmetric quantum mechanics, Topological origin of quantum mechanical vacuum transitions and tunneling, Constant curvature surfaces of the supersymmetric ℂP N−1 sigma model, The energy of scattering solitons in the Ward model, Instantons on hyperbolic four-space, Skyrmions and the α-particle model of nuclei, Hyperbolic vortices and Dirac fields in 2+1 dimensions, Structural equations of supermanifolds immersed in the superspace ${\mathcal{M}^{(3\vert2)}(c)}$ with a prescribed curvature, Analysis of the adiabatic limit for solitons in classical field theory, Topology and energy of time-dependent unitons, Hopfions in chiral magnets, On the tetrahedrally symmetric monopole, Gauss-Bonnet boson stars, Deformed self-dual magnetic monopoles, Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals, Gravity of a noncanonical global monopole: conical topology and compactification, Kink–antikink scattering-induced breathing bound states and oscillons in a parametrized ϕ4 model, Quasi-Integrability and Some Aspects of SU(3) Toda Field Theory, HOPF SOLITON SOLUTIONS FROM LOW ENERGY EFFECTIVE ACTION OF SU(2) YANG–MILLS THEORY, Yang–Mills instanton sheaves with higher topological charges, Forces between kinks and antikinks with long-range tails, Exact moduli space metrics for hyperbolic vortex polygons, Nonexistence of Skyrmion–Skyrmion and Skyrmion–anti-Skyrmion static equilibria, Constant Curvature Holomorphic Solutions of the Supersymmetric G(2, 4) Sigma Model, Solitons in complex systems of chiral fields with Kuramoto interactions, Geometry and energy of non-Abelian vortices, Scalar geons in Born-Infeld gravity, Classical transitions with the topological number changing in the early Universe, Kink–antikink interaction forces and bound states in a biharmonic ϕ ⁴ model, Some novel considerations about the collective coordinates approximation for the scattering of ϕ ⁴ kinks, Nineteen vortex equations and integrability, The moduli space of non-abelian vortices in Yang–Mills–Chern–Simons–Higgs theory, Stability of solitary waves in nonlinear Klein–Gordon equations, Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory, Compact Q-balls, The volume of a soliton, GRAVITY-ASSISTED SOLUTION OF THE MASS GAP PROBLEM FOR PURE YANG–MILLS FIELDS, Soliton stability in some knot soliton models, Conservation laws in Skyrme-type models, Scattering for the Klein-Gordon equation with quadratic and variable coefficient cubic nonlinearities, The adiabatic limit of wave map flow on a two-torus, Moduli space dynamics of noncommutative $U(2)$ instantons, Trapping spin-0 particles on p-balls in $(D, 1)$ dimensions, Characteristic analysis for integrable soliton models on two-dimensional target spaces, Kink excitation spectra in the $(1+1)$-dimensional $\phi^{8}$ model, Resurgence in sine-Gordon quantum mechanics: exact agreement between multi-instantons and uniform WKB, Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles, A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges, Classical Skyrmions-static solutions and dynamics, WAVE-PACKET SCATTERING OFF THE KINK-SOLUTION, Kink-antikink collisions and multi-bounce resonance windows in higher-order field theories, Particle-based numerical modeling of a thin granular layer subjected to oscillating flow, Integrable abelian vortex-like solitons, Topological first-order vortices in a gauged $CP(2)$ model, New soliton solutions of anti-self-dual Yang-Mills equations, Split Q-balls, Hopfions interaction from the viewpoint of the product ansatz, Symmetric calorons of higher charges and their large period limits, A point particle model of lightly bound skyrmions, Symmetric calorons and the rotation map, Asymptotic stability analysis for $\mathrm{SU}(n)$ dark monopoles, Asymptotic stability for odd perturbations of the stationary kink in the variable-speed 𝜙⁴ model, Moduli spaces of lumps on real projective space, Vortices in vacuumless systems, Orbital stability and instability of periodic wave solutions for the $\phi^4$-model, Wobbling kinks in a two-component scalar field theory: interaction between shape modes, Non-perturbative aspects of the self-dual double copy, Kink-antikink collision in the supersymmetric $\phi^4$ model, BPS skyrmions of generalized Skyrme model in higher dimensions, Asymptotic methods for soliton excitations, The ${\phi}^4$ model with the BPS preserving defect, Moduli space with a boundary, Kinks in higher-order polynomial models, Scattering of kinks in the $B\varphi^4$ model, Collisions of kinks in deformed $\varphi^4$ and $\varphi^6$ models, WARPED COMPACTIFICATION ON SIGMA MODEL, SKYRMIONS IN SIX DIMENSIONS, Cuscuton kinks and branes, Quantum nucleation of topological solitons, Compact kink and its interaction with compact oscillons, Interacting kinks and meson mixing, Fundamental group and fine topology on Minkowski space, Near-BPS skyrmions, Electroweak multi-monopoles, Resonance mediated by fermions in kink-antikink collisions, Fermionic spectral walls in kink collisions, Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms, Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space, Abelian Hopfions of the $\mathbb{CP}^n$ model on $\mathbb{R}^{2n+1}$ and a fractionally powered topological lower bound, Platonic hyperbolic monopoles, Winding Hopfions on $R^2{\times}S^1$, Existence of non-Abelian vortices with product gauge groups, Quantum SU(3) Skyrme model with noncanonical embedded SO(3) soliton, Five vortex equations, Non-abelian self-dual strings in six dimensions from four dimensional 1/2-BPS monopoles, Propagation of Twist Solitons in Fully Inhomogeneous DNA Chains, A NOTE ON THE EXISTENCE OF SOLITON SOLUTIONS IN THE CHERN–SIMONS–CP(1) MODEL, Exact meron black holes in four dimensional $\mathrm{SU}(2)$ Einstein-Yang-Mills theory, Statics and dynamics of magnetic vortices and of Nielsen–Olesen (Nambu) strings, Kinks, chains, and loop groups in the CPn sigma models, Vortices and monopoles in mass-deformed $\mathrm{SO}$ and $\mathrm{USp}$ gauge theories, Small horizons, Gauge fields, strings, solitons, anomalies, and the speed of life, Dual infrared limits of 6d $\mathcal{N} = (2, 0)$ theory, $\mathbb{C}P^{2S}$ sigma models described through hypergeometric orthogonal polynomials, Dispersive decay for the 1D Klein-Gordon equation with variable coefficient nonlinearities, GAUGE THEORY OF FADDEEV–SKYRME FUNCTIONALS, Q-balls in the $U(1)$ gauged Friedberg-Lee-Sirlin model, No skyrmion hair for stationary spherically symmetric reflecting stars, On the charge density and asymptotic tail of a monopole, General solutions of the supersymmetric ℂP2 sigma model and its generalisation to ℂP N−1, Iterated $\varphi^4$ kinks, Black magic session of concordance: Regge mass spectrum from Casson’s invariant, Ginzburg-Landau equations on Riemann surfaces of higher genus, Skyrme and Faddeev models in the low-energy limit of 4D Yang-Mills-Higgs theories, Conditional stable soliton resolution for a semi-linear Skyrme equation, Self-gravitating skyrmions, IMPROVED APPROXIMATE PROFILE FUNCTION OF HEDGEHOG SKYRMION, Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect, Scaling identities for solitons beyond Derrick’s theorem, Vortices in a generalized Maxwell-Higgs model with visible and hidden sectors, Moduli Space of Non-Abelian Vortices, Curvature-stabilized skyrmions with angular momentum, Bogomolny-Prasad-Sommerfeld monopoles and open spin chains, Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear $\sigma$-model system: black holes with NUT, black strings and time-dependent solutions, Analytical BPS Maxwell-Higgs vortices, Interactions of $B = 4$ Skyrmions, Knot topology in QCD, The Kähler potential of Abelian Higgs vortices, Near BPS skyrmions and restricted harmonic maps, Existence theorems for non-abelian Chern-Simons-Higgs vortices with flavor, Kinklike structures in scalar field theories: from one-field to two-field models, Self-dual soliton solutions in a Chern–Simons-CP(1) model with a nonstandard kinetic term, Orbit based procedure for doublets of scalar fields and the emergence of triple kinks and other defects, From kinks to compactons