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Tang, Bo; He, Yinnian; Wei, Leilei; Wang, Shaoli

Variable-coefficient discrete \((\frac{G^{\prime}}{G})\)-expansion method for nonlinear differential-difference equations. (English) Zbl 1252.37062

Phys. Lett., A 375, No. 38, 3355-3361 (2011).
Summary: In this Letter, a variable-coefficient discrete \((\frac{G^{\prime}}{G})\)-expansion method is proposed to seek new and more general exact solutions of nonlinear differential-difference equations. Being concise and straightforward, this method is applied to the (2+1)-dimension Toda equation. As a result, many new and more general exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear differential-difference equations in mathematical physics.

Cited in 6 Documents

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
41A10 Approximation by polynomials
41A20 Approximation by rational functions
42A10 Trigonometric approximation
35C09 Trigonometric solutions to PDEs
33B10 Exponential and trigonometric functions

Keywords:

nonlinear differential-difference equation; variable-coefficient discrete \((\frac{G^{\prime}}{G})\)-expansion method; hyperbolic function solution; trigonometric function solution; rational solution
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References:

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