Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws

DOI10.1007/978-3-540-89199-4_16zbMath1230.37084OpenAlexW1527793196MaRDI QIDQ3654741

Publication date: 11 January 2010

Published in: Springer Tracts in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-89199-4_16

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Lattice dynamics; integrable lattice equations (37K60)

Cites Work

From integrable lattices to non-QRT mappings
On a class of spatial discretizations of equations of the nonlinear Schrödinger type
Discrete nonlinear Schrödinger equations free of the Peierls-Nabarro potential
Iteration of some discretizations of the nonlinear Schrödinger equation
On a class of discretizations of Hamiltonian nonlinear partial differential equations
Bushes of vibrational modes for Fermi-Pasta-Ulam chains
Integrable mappings and soliton equations. II
Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity: Existence, stability and dynamics
Bifurcation analysis of the localized modes dynamics in lattices with saturable nonlinearity
How to find the conserved quantities of nonlinear discrete equations
Translationally invariant nonlinear Schrödinger lattices
Exact stationary solutions for the translationally invariant discrete nonlinear Schrödinger equations
Domain wall and periodic solutions of coupled ϕ4 models in an external field
A discrete $\phi^4$ system without a Peierls - Nabarro barrier
Nonlinear differential−difference equations
Nonlinear differential–difference equations and Fourier analysis
Continuum limit of lattice approximation schemes
Exact solutions of the saturable discrete nonlinear Schrödinger equation
Topological discrete kinks
Kink dynamics in a novel discrete sine-Gordon system
Exact static solutions to a translationally invariant discrete phi⁴model
Exact moving and stationary solutions of a generalized discrete nonlinear Schrödinger equation
Travelling kinks in discrete phi⁴models
Standard nearest-neighbour discretizations of Klein–Gordon models cannot preserve both energy and linear momentum
Kinks in dipole chains
Discrete Klein–Gordon models with static kinks free of the Peierls–Nabarro potential

This page was built for publication: Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws