scientific article

Publication date: 27 October 2011

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

cubic nonlinear term nonlinear Dirac equation Bloch bands discrete NLS equation bandgap periodic linear potentials

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Soliton equations (35Q51) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Soliton solutions (35C08)

Related Items (67)

Nonlinear wave dynamics near phase transition in \(\mathcal{PT}\)-symmetric localized potentials ⋮ Transverse instability of line solitary waves in massive Dirac equations ⋮ Loops of Energy Bands for Bloch Waves in Optical Lattices ⋮ Periodic waves in the fractional modified Korteweg-de Vries equation ⋮ Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation ⋮ On the instability of the Ruf-Sani solitons for the NLS with exponential nonlinearity ⋮ Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem ⋮ Nonlinear Stark--Wannier Equation ⋮ Existence of discrete solitons in discrete nonlinear Schrödinger equations with non-weak couplings ⋮ Validity of the NLS approximation for periodic quantum graphs ⋮ Spectral stability of periodic waves in the generalized reduced Ostrovsky equation ⋮ Arbitrary high-order exponential integrators conservative schemes for the nonlinear Gross-Pitaevskii equation ⋮ Spatially localized structures in lattice dynamical systems ⋮ Coupled mode equations and gap solitons in higher dimensions ⋮ A comment about the paper ``On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation ⋮ Stability of symmetric vortices for two-component Ginzburg-Landau systems ⋮ Nonlinear dynamics of modulated waves on graphene like quantum graphs ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ Oscillatory instabilities of gap solitons in a repulsive Bose-Einstein condensate ⋮ Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study ⋮ Plane wave stability analysis of Hartree and quantum dissipative systems ⋮ Bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger equations ⋮ Stability of smooth periodic travelling waves in the Camassa–Holm equation ⋮ On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation ⋮ On nonexistence of continuous families of stationary nonlinear modes for a class of complex potentials ⋮ Perturbation theory for nonlinear Schrödinger equations ⋮ Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity ⋮ Chern-Simons-Schrödinger theory on a one-dimensional lattice ⋮ Strong non-monotonic behavior of particle density of solitary waves of nonlinear Schrödinger equation in Bose-Einstein condensates ⋮ Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices ⋮ Stationary hypergeometric solitons and their stability in a Bose-Einstein condensate with \(\mathcal{PT}\)-symmetric potential ⋮ On the Global Behavior of Solutions of a Coupled System of Nonlinear Schrödinger Equation ⋮ A symplectic perspective on constrained eigenvalue problems ⋮ Orbital stability of Dirac solitons ⋮ On transverse stability of discrete line solitons ⋮ Modulated solitons, soliton and vortex clusters in purely nonlinear defocusing media ⋮ On the validity of the variational approximation in discrete nonlinear Schrödinger equations ⋮ NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝ^d ⋮ Justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear Schrödinger equation ⋮ Construction of solutions for some localized nonlinear Schrödinger equations ⋮ Bifurcations of standing localized waves on periodic graphs ⋮ Existence of dark solitons in discrete nonlinear Schrödinger equations with non-weak couplings ⋮ Orbital stability in the cubic defocusing NLS equation. I: Cnoidal periodic waves ⋮ Wave packet dynamics in slowly modulated photonic graphene ⋮ Numerical analyses for spectral stability of solitary waves near bifurcation points ⋮ Nonlinear models and bifurcation trees in quantum mechanics: a review of recent results ⋮ A Normal Form for Hamiltonian--Hopf Bifurcations in Nonlinear Schrödinger Equations with General External Potentials ⋮ Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential ⋮ Derivation of the tight-binding approximation for time-dependent nonlinear Schrödinger equations ⋮ Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with 𝒫𝒯-symmetry ⋮ Existence and Stability of Klein–Gordon Breathers in the Small-Amplitude Limit ⋮ Stationary states for nonlinear Schrödinger equations with periodic potentials ⋮ Justification of a nonlinear Schrödinger model for laser beams in photopolymers ⋮ Wannier functions and discrete NLS equations for nematicons ⋮ The nonlinear Dirac equation in Bose–Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices ⋮ Standing lattice solitons in the discrete NLS equation with saturation ⋮ Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation ⋮ Numerical computations for bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger equations ⋮ Wave Packets in the Fractional Nonlinear Schrödinger Equation with a Honeycomb Potential ⋮ Nonlinear optical waveguide lattices: asymptotic analysis, solitons, and topological insulators ⋮ Critical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations ⋮ ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED ⋮ Morse index for the ground state in the energy supercritical Gross-Pitaevskii equation ⋮ Stationary solutions to cubic nonlinear Schrödinger equations with quasi-periodic boundary conditions ⋮ The One-Dimensional Dirac Equation With Concentrated Nonlinearity ⋮ Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems ⋮ On a mathematical model for a damped and driven double-well Bose-Einstein condensate

This page was built for publication: