Automated derivation of the conservation laws for nonlinear differential-difference equations

DOI10.1007/s11424-012-9297-zzbMath1286.34020OpenAlexW2045545006MaRDI QIDQ394413

Jiaofeng Zhu, Yin-Ping Liu

Publication date: 27 January 2014

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-012-9297-z

zbMATH Keywords

conservation lawsintegrabilityscaling invariancedifferential-difference equationsautomated derivation

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04) Ordinary lattice differential equations (34A33)

Uses Software

• CONSLAW
• GeM
• Maple
• CLawDDEs
• DDESpecialSolutions
• CONDENS
• JACOBI

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations
• GeM software package for computation of symmetries and conservation laws of differential equations
• Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations
• An algorithm for the complete symmetry classification of differential equations based on Wu's method
• Theory of nonlinear lattices
• Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions
• A differential-difference equation for a KdV-MKdV equation
• The conservation laws of some discrete soliton systems.
• Symmetry and integration methods for differential equations
• Computation of conserved densities for systems of nonlinear differential-difference equations
• Multi-component Volterra and Toda type integrable equations
• A generalized coth-function method for exact solution of differential-difference equation
• CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations
• An integrability test for differential-difference systems
• A Nonlinear Difference Scheme and Inverse Scattering
• Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications
• Direct construction method for conservation laws of partial differential equations Part II: General treatment