A symbolic computational method for constructing exact solutions to difference-differential equations

DOI10.1016/j.amc.2005.11.060zbMath1100.65083OpenAlexW2088170105MaRDI QIDQ2507837

Wang Zhen, Hong-Qing Zhang

Publication date: 5 October 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.11.060

zbMATH Keywords

periodic solutionsfinite difference methoddifference equationsexact solutionsrational solutionssoliton solutionsToda equationtanh methodToda lattice equationprojective Riccati equationnonlinear partial difference-differential equationsymbolic system Maple

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Partial functional-differential equations (35R10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Soliton equations (35Q51) Additive difference equations (39A10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (10)

Generalizing homotopy analysis method to solve Lotka-Volterra equation ⋮ Construct solitary solutions of discrete hybrid equation by Adomian decomposition method ⋮ Generalized differential transform method to differential-difference equation ⋮ The \(\left(\frac{G^\prime}{G}\right)\)-expansion method for the nonlinear lattice equations ⋮ Adomian decomposition and Padé approximate for solving differential-difference equation ⋮ Solution of the differential-difference equations by optimal homotopy asymptotic method ⋮ Extended mixed function method and its application for solving two classic Toda lattice equations ⋮ Mixed function method for obtaining exact solution of nonlinear differential-difference equations and coupled NDDEs ⋮ Applying homotopy analysis method for solving differential-difference equation ⋮ Solving the discrete KdV equation with homotopy analysis method

Uses Software

• Maple
• DDESpecialSolutions

Cites Work

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• On the integrability of systems of nonlinear ordinary differential equations with superposition principles
• Link between solitary waves and projective Riccati equations
• The inverse scattering transform: Semi-infinite interval
• A Nonlinear Difference Scheme and Inverse Scattering
• Do integrable mappings have the Painlevé property?
• Painlevé analysis and integrability properties of a 2+1 nonrelativistic field theory
• A Search for Higher-Dimensional Integrable Modified KdV Equations The Painlevé Approach
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

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