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Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions - MaRDI portal

Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions (Q2680016)

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Language	Label	Description	Also known as
English	Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions	scientific article

Statements

scholarly article

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Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions (English)

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Chaos, Solitons and Fractals

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publication date

26 January 2023

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zbMATH Keywords

nonlinear differential-difference hierarchy

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Lax pair

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conservation laws

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\(N\)-fold Darboux transformation

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explicit exact solutions

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/j.chaos.2022.112460

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Chaos and localization in the discrete nonlinear Schrödinger equation

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A class of solutions of the two-dimensional Toda lattice equation

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Toda lattice hierarchy and soliton equations on square lattice

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PreHamiltonian and Hamiltonian operators for differential-difference equations

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Rational W-shape solitons on a nonlinear electrical transmission line with Josephson junction

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Standing lattice solitons in the discrete NLS equation with saturation

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Discovery of lattice soliton

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Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants

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Reductions of the Volterra lattice

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Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice

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Stationary multi-kinks in the discrete sine-Gordon equation

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Modulated wave and modulation instability gain brought by the cross-phase modulation in birefringent fibers having anti-cubic nonlinearity

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Vector bright soliton interactions of the two-component AB system in a baroclinic fluid

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Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation

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Shallow-water-wave studies on a (2 + 1)-dimensional Hirota-Satsuma-Ito system: \(X\)-type soliton, resonant \(Y\)-type soliton and hybrid solutions

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Generalized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order nonlinear Schrödinger system in a birefringent optical fiber

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Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics

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Hybrid solutions for the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics

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Matrix spectral problems and integrability aspects of the Błaszak-Marciniak lattice equations

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Construction of solutions for an integrable differential-difference equation by Darboux-Bäcklund transformation

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Integrable discretizations and soliton solutions of an Eckhaus-Kundu equation

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Bäcklund transformation and multi-soliton solutions for the discrete Korteweg-de Vries equation

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Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system

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Geometric series method and exact solutions of differential-difference equations

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Inverse scattering transform for the defocusing Ablowitz–Ladik system with arbitrarily large nonzero background

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The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy

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The discrete tanh method for solving the nonlinear differential-difference equations

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Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations

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Taking into consideration an extended coupled (2+1)-dimensional Burgers system in oceanography, acoustics and hydrodynamics

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Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber

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Optical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger system

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Lie group analysis for a higher-order Boussinesq-Burgers system

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Considering the shallow water of a wide channel or an open sea through a generalized \((2+1)\)-dimensional dispersive long-wave system

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Higher-order hybrid waves for the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation for an irrotational incompressible fluid via the modified Pfaffian technique

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Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended \((3+1)\)-dimensional nonlinear Schrödinger equation in an optical fiber

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Water-wave studies on a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system

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Magnetohydrodynamics and fluid dynamics: action principles and conservation laws

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Bilinear Bäcklund transformation, <i>N</i>‐soliton, and infinite conservation laws for Lax–Kadomtsev–Petviashvili and generalized Korteweg–de Vries equations

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A generating scheme for conservation laws of discrete zero curvature equations and its application

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A Darboux transformation for the Volterra lattice equation

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Positive and negative integrable lattice hierarchies: conservation laws and \(N\)-fold Darboux transformations

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Nonlinear differential–difference equations and Fourier analysis

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The robust inverse scattering method for focusing Ablowitz-Ladik equation on the non-vanishing background

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Modulational instability and dynamics of multi-rogue wave solutions for the discrete Ablowitz-Ladik equation

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Nonlocal reductions of the Ablowitz-Ladik equation

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A generalized Ablowitz–Ladik hierarchy, multi-Hamiltonian structure and Darboux transformation

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Identifiers

10.1016/j.chaos.2022.112460

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2680016

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