Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations

DOI10.1016/J.CAMWA.2009.01.008zbMath1186.33039OpenAlexW2011514823MaRDI QIDQ971603

Xin Zeng, Xue-Lin Yong, Yu-Fu Chen, Zhi Yong Zhang

Publication date: 16 May 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.01.008

zbMATH Keywords

symbolic computationexact solutionsJacobi elliptic functionsdifferential-difference equations

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Explicit solutions, first integrals of ordinary differential equations (34A05) Elliptic functions and integrals (33E05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Ordinary lattice differential equations (34A33)

Related Items (5)

The periodic solutions to Kawahara equation by means of the auxiliary equation with a sixth-degree nonlinear term ⋮ Automated derivation of the conservation laws for nonlinear differential-difference equations ⋮ Application of the \(G^{\prime}/G\)-expansion method to Kawahara type equations using symbolic computation ⋮ JACOBI ⋮ Observations on the class of ``Balancing Principle for nonlinear PDEs that can be treated by the auxiliary equation method

Uses Software

• Maple
• DDESpecialSolutions

Cites Work

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• Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations
• Jacobian elliptic function method for nonlinear differential-difference equations
• New Jacobi elliptic function solutions of the semi-discrete coupled mKdV system
• Multi-component Volterra and Toda type integrable equations
• Nonlinear differential−difference equations
• Nonlinear Evolution Equations—Continuous and Discrete
• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
• Conditions for the existence of higher symmetries of evolutionary equations on the lattice
• Variable separation approach for a differential-difference system: special Toda equation

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