Dynamics of bright and dark multi-soliton solutions for two higher-order Toda lattice equations for nonlinear waves
type: Item
instance of: scholarly article
title: Dynamics of bright and dark multi-soliton solutions for two higher-order Toda lattice equations for nonlinear waves
zbMATH Open document ID: 1448.37085
author: Nan Liu
author: Xiao-Yong Wen
author: Ling Xu
published in: Advances in Difference Equations
publication date: 2019-01-25T00:00:00Z
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K40
zbMATH DE Number: 7006921
zbMATH Keywords: higher-order Toda lattice equation
zbMATH Keywords: discrete \(N\)-fold Darboux transformation
zbMATH Keywords: discrete bright and dark multi-soliton solutions
zbMATH Keywords: rational solutions
zbMATH Keywords: numerical simulations
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: s13662-018-1748-y
OpenAlex ID: W2888242788
cites work: A Nonlinear Difference Scheme and Inverse Scattering
cites work: Nonlinear differential−difference equations
cites work: Nonlinear Evolution Equations—Continuous and Discrete
cites work: Q3995225
cites work: Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
cites work: Generalised (2+1)-dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory
cites work: A new integrable symplectic map by the binary nonlinearization to the super AKNS system
cites work: Long-time asymptotics and the bright \(N\)-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach
cites work: Integrability and exact solutions of a two-component Korteweg-de Vries system
cites work: Theory of nonlinear lattices.
cites work: Variational solutions for the discrete nonlinear Schrödinger equation
cites work: Binary Bargmann symmetry constraint associated with 3×3 discrete matrix spectral problem
cites work: A new integrable symplectic map and the Lie point symmetry associated with nonlinear lattice equations
cites work: A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy
cites work: Q3732103
cites work: On the Toda Lattice. II: Inverse-Scattering Solution
cites work: Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices
cites work: Bäcklund transformation solutions of the Toda lattice equation
cites work: Nonlinear partial difference equations. IV: Bäcklund transformations for the discrete-time Toda equation
cites work: The reduction problem and the inverse scattering method
cites work: Q4002235
cites work: Dressing procedure for solutions of non-linear equations and the method of operator identities
cites work: Algebraic construction of the Darboux matrix revisited
cites work: Q4854012
cites work: Darboux transformations in integrable systems. Theory and their applications to geometry
cites work: Darboux transformation and Crum's formula for multi-component integrable equations
cites work: Reduction groups and related integrable difference systems of nonlinear Schrödinger type
cites work: Soliton solutions by Darboux transformation for a Hamiltonian lattice system
cites work: Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4×4 Lax pairs
cites work: N-fold Darboux transformation and soliton solutions for Toda lattice equation
cites work: \(N\)-fold Darboux transformation and solitonic interactions for a Volterra lattice system
cites work: Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability
cites work: Modulational instability and higher order-rogue wave solutions for the generalized discrete Hirota equation
cites work: A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and Darboux transformation
cites work: Two integrable lattice hierarchies and their respective Darboux transformations
cites work: A trace identity and its applications to the theory of discrete integrable systems
cites work: The conservation laws of some discrete soliton systems.
cites work: The Toda lattice. II. Existence of integrals
cites work: New classes of Toda soliton solutions
cites work: An operator-theoretic approach to the Toda lattice equation
cites work: Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
cites work: Soliton solution of three differential-difference equations in Wronskian form
cites work: Rational solutions of the Toda lattice equation in Casoratian form
cites work: A KIND OF EXPLICIT QUASI-PERIODIC SOLUTION AND ITS LIMIT FOR THE TODA LATTICE EQUATION
cites work: Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method
cites work: Nonlinear Waves in Integrable and Nonintegrable Systems
cites work: Spectral Methods in MATLAB
DOI: 10.1186/S13662-018-1748-Y
description: scientific article; zbMATH DE number 7006921