zbMath1061.37056MaRDI QIDQ4423191
Helge Holden, Friedrich Gesztesy
Publication date: 26 August 2003
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)
Soliton equations (35Q51)
Relationships between algebraic curves and integrable systems (14H70)
Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)
Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)
Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)
Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)
On Doubly Periodic Standing Wave Solutions of the Coupled Higgs Field Equation,
The algebro-geometric solutions for the Fokas-Olver-Rosenau-Qiao (FORQ) hierarchy,
Algebro-geometric solutions for the Ruijsenaars-Toda hierarchy,
Trace Formulas for Schrödinger Operators in Connection with Scattering Theory for Finite-gap Backgrounds,
Parametric solutions of the generalized short pulse equations,
Analytic Riemann Theta Function Solutions of Coupled Korteweg-de Vries Hierarchy,
Algebro-geometric solutions for the complex Sharma-Tasso-Olver hierarchy,
The inverse scattering transform for weak Wigner–von Neumann type potentials *,
Trigonal curves and algebro-geometric solutions to soliton hierarchies I,
A Dispersive Regularization for the Modified Camassa--Holm Equation,
A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$,
Arnold--Liouville Theorem for Integrable PDEs: A Case Study of the Focusing NLS Equation,
Algebro-geometric constructions of the Heisenberg hierarchy,
ABC of ladder operators for rationally extended quantum harmonic oscillator systems,
Reduced nonlocal integrable mKdV equations of type (−λ, λ) and their exact soliton solutions,
A Riemann-Hilbert method to algebro-geometric solutions of the Korteweg-de Vries equation,
Deformation of the spectrum for Darboux-Treibich-Verdier potential along \(\mathrm{Re}\,\tau =\frac{1}{2}\),
Integrable nonlocal nonlinear Schrödinger hierarchies of type \((-\lambda*,\lambda)\) and soliton solutions,
Burchnall-Chaundy polynomials for matrix ODOs and Picard-Vessiot theory,
Elliptic KdV potentials and conical metrics of positive constant curvature. I,
Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation,
Application of tetragonal curves to coupled Boussinesq equations,
The quasi-periodic Cauchy problem for the generalized Benjamin-Bona-Mahony equation on the real line,
Uniform Estimate of Potentials by Reflection Coefficients and its Application to KdV Flow,
Dressing for Fokker-Planck Equations: the Cases of 1+1 and 1+ℓ Dimensions,
On the integrable symplectic map and the \(N\)-soliton solution of the Toda lattice,
Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions,
A hierarchy of generalized Jaulent–Miodek equations and their explicit solutions,
Elliptic finite-band potentials of a non-self-adjoint Dirac operator,
Multisolitons are the unique constrained minimizers of the KdV conserved quantities,
Soliton solutions to constrained nonlocal integrable nonlinear Schrödinger hierarchies of type (−λ,λ),
Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes,
Quasi-periodic solutions to a negative-order integrable system of 2-component KdV equation,
Algebro-geometric constructions of a hierarchy of integrable semi-discrete equations,
Linear systems, Hankel products and the sinh-Gordon equation,
Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations,
An explicit characterization of Calogero–Moser systems,
Soliton Equations and Their Holomorphic Solutions,
Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz–Ladik Hierarchy,
KdV hierarchy via Abelian coverings and operator identities,
Algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy,
Nonlinear differential identities for cnoidal waves,
Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation,
Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems,
Quasiperiodic Wave Solutions of Supersymmetric KdV Equation in Superspace,
AKNS and NLS hierarchies, MRW solutions, P n breathers, and beyond,
A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants,
Algebro-geometric constructions of the Wadati-Konno-Ichikawa flows and applications,
Computing periods of hypersurfaces,
Spectral analysis for one class of second-order indefinite non-self-adjoint differential operator pencil,
Quasi-Periodic Solutions of Coupled KDV Type Equations, [
https://portal.mardi4nfdi.de/wiki/Publication:5230893 Hyperelliptic function solutions with finite genus ������ of coupled nonlinear differential equations*],
Algebro-Geometric Solutions and Their Reductions for the Fokas-Lenells Hierarchy,
Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy,
On a spectral analysis of scattering data for the Camassa-Holm equation,
Finite genus solutions for Geng hierarchy,
GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS,
Quasi-Periodic Solutions of Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem,
The Application of Neumann Type Systems for Solving Integrable Nonlinear Evolution Equations,
Self-Isospectrality, Special Supersymmetry, and their Effect on the Band Structure,
A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy,
Soliton solutions and quasiperiodic solutions of modified Korteweg–de Vries type equations,
Conservative solutions for higher-order Camassa–Holm equations,
The effect of a positive bound state on the KdV solution: a case study *,
Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions,
Finite-gap solutions of 2+1 dimensional integrable nonlinear evolution equations generated by the Neumann systems,
Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators,
Algebro-geometric solutions to the lattice potential modified Kadomtsev–Petviashvili equation,
Effective integration of ultra-elliptic solutions of the focusing nonlinear Schrödinger equation,
Algebro-geometric solutions of the generalized Burgers hierarchy associated with a \(3\times 3\) matrix spectral problem based on Riemann surface,
Cnoidal waves on Fermi-Pasta-Ulam lattices,
The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions,
Almost periodicity in time of solutions of the KdV equation,
Bilinear Bäcklund transformations and explicit solutions of a \((3+1)\)-dimensional nonlinear equation,
Type \(( - \lambda, - \lambda^\ast)\) reduced nonlocal integrable mKdV equations and their soliton solutions,
The inverse problem method on the half-line and a nested system of Riccati equations,
The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation,
Nonlocal integrable mKdV equations by two nonlocal reductions and their soliton solutions,
Wannier functions for quasiperiodic finite-gap potentials,
Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators,
Well-posedness of higher-order Camassa-Holm equations,
Riemann-Hilbert problems of a six-component mKdV system and its soliton solutions,
The complex Hamiltonian system in the Gerdjikov-Ivanov equation and its applications,
Riemann-Hilbert problems and soliton solutions of nonlocal reverse-time NLS hierarchies,
Algebro-geometric solutions for the two-component Camassa-Holm Dym hierarchy,
Spectral properties of a class of reflectionless Schrödinger operators,
The matrix-resolvent method to tau-functions for the nonlinear Schrödinger hierarchy,
Long-time asymptotics of perturbed finite-gap Korteweg-de Vries solutions,
Algebro-geometric solutions of the Harry Dym hierarchy,
Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system,
Formation of the undular bores in shallow water generalized Kaup-Boussinesq model,
Quasi-periodic solutions of the Kaup-Kupershmidt hierarchy,
Effective integration of the nonlinear vector Schrödinger equation,
Algebro-geometric solutions of the TD hierarchy,
The Riemann-Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient \((2+1)\)-dimensional KdV equation,
Super quasiperiodic wave solutions and asymptotic analysis for \(\mathcal N=1\) supersymmetric KdV-type equations,
Super Riemann theta function periodic wave solutions and rational characteristics for a supersymmetric KdV-Burgers equation,
A new spectral problem and the related integrable nonlinear evolution equations,
Inverse scattering for nonlocal reverse-time nonlinear Schrödinger equations,
Quasiperiodic solutions of the Kadomtsev-Petviashvili equation via the multidimensional Baker-Akhiezer function generated by the Broer-Kaup hierarchy,
Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy,
Riemann theta function solutions of the Caudrey-Dodd-Gibbon-Sawada-Kotera hierarchy,
Bounded ultra-elliptic solutions of the defocusing nonlinear Schrödinger equation,
Global existence for a new periodic integrable equation.,
Factorization of KdV Schrödinger operators using differential subresultants,
A numerical study of the 3-periodic wave solutions to KdV-type equations,
The transformation operator for Schrödinger operators on almost periodic infinite-gap backgrounds,
KdV equation beyond standard assumptions on initial data,
Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations,
The Neumann type systems and algebro-geometric solutions of a system of coupled integrable equations,
Self-isospectral tri-supersymmetry in \(\mathcal P \mathcal T\)-symmetric quantum systems with pure imaginary periodicity,
The special class of second integrals of the KdV equation,
Algebro-geometric solutions of the Dirac hierarchy,
Finite gap Jacobi matrices. I: The isospectral torus,
Computing new solutions of algebro-geometric equation using the discrete inverse Sumudu transform,
Riemann-Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions,
Bäcklund transformation and quasi-periodic solutions for a variable-coefficient integrable equation,
New types of doubly periodic standing wave solutions for the coupled Higgs field equation,
Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method,
Inverse scattering for reflectionless Schrödinger operators with integrable potentials and generalized soliton solutions for the KdV equation,
Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies,
Finite genus solutions to the coupled Burgers hierarchy,
On the trace-class property of Hankel operators arising in the theory of the Korteweg-de Vries equation,
Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves,
Darboux transformation and conservation laws of a integrable evolution equations with \(3 \times 3\) Lax pairs,
Tau functions associated with linear systems,
Coupled discrete Sawada-Kotera equations and their explicit quasi-periodic solutions,
Algebro-geometric solutions of the coupled Chaffee-Infante reaction diffusion hierarchy,
A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law,
Riemann-Hilbert problems and soliton solutions of nonlocal real reverse-spacetime mKdV equations,
Gross-Neveu models, nonlinear Dirac equations, surfaces and strings,
Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices,
Trace formulas for non-self-adjoint periodic Schrödinger operators and some applications,
Two-phase periodic solutions to the AKNS hierarchy equations,
Quasi-periodic solutions of mixed AKNS equations,
A two-component generalization of Burgers' equation with quasi-periodic solution,
Algebro-geometric solutions for the derivative Burgers hierarchy,
On quasiperiodic solutions of the modified Kadomtsev-Petviashvili hierarchy,
A kind of explicit Riemann theta functions periodic waves solutions for discrete soliton equations,
Theta function solutions for two discrete equations,
Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions,
Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations,
Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background,
Quasi-periodic solutions of the Heisenberg hierarchy,
Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial function,
The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions,
Explicit quasi-periodic solutions of the Kaup-Newell hierarchy,
Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials,
Explicit solutions of the coupled Bogoyavlensky lattice 1(2) Hierarchy,
Restrictions on the existence of a canonical system flow hierarchy,
Algebro-geometric solutions for the Hunter-Saxton hierarchy,
On algebro-geometric simply-periodic solutions of the KdV hierarchy,
Camassa-Holm cuspons, solitons and their interactions via the dressing method,
Aharonov-Bohm effect on AdS\(_2\) and nonlinear supersymmetry of reflectionless Pöschl-Teller system,
The expansions of spectral function and the corresponding finite dimensional integrable systems,
Riemann-Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies,
An exactly solvable problem of wave fronts and applications to the asymptotic theory,
Spectral analysis of Darboux transformations for the focusing NLS hierarchy,
On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV poten\-tials,
Rational KdV potentials and differential Galois theory,
Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows,
The Bogoliubov-de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry,
Algebro-geometric solutions of the Baxter-Szegő difference equation,
An alternative approach to solve the mixed AKNS equations,
On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data. II: Perturbations with finite moments,
Generalized reflection coefficients,
A multi-component integrable hierarchy and its integrable reductions,
Spectral Picard-Vessiot fields for algebro-geometric Schrödinger operators