A Riemann theta function formula with its application to double periodic wave solutions of nonlinear equations

Details A Riemann theta function formula with its application to double periodic wave solutions of nonlinear equations A Riemann theta function formula with its application to double periodic wave solutions of nonlinear equations

2010-01-13

arxiv.org/abs/1001.2159v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages

Scientific paper

Based on a Riemann theta function and Hirota's bilinear form, a lucid and straightforward way is presented to explicitly construct double periodic wave solutions for both nonlinear differential and difference equations. Once such a equation is written in a bilinear form, its periodic wave solutions can be directly obtained by using an unified theta function formula. The relations between the periodic wave solutions and soliton solutions are rigorously established. The efficiency of our proposed method can be demonstrated on a class variety of nonlinear equations such as those considered in this paper, shall water wave equation, (2+1)-dimensional Bogoyavlenskii-Schiff equation and differential-difference KdV equation.

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