An elliptic equation method and its applications in nonlinear evolution equations. (English) Zbl 1142.35587

Xu, Guiqiong

Chaos Solitons Fractals 29, No. 4, 942-947 (2006).

Summary: An elliptic equation method is presented for constructing new types of elliptic function solutions of nonlinear evolution equations. The key idea of this method is to use solutions of an elliptic equation involving four real distinct roots to construct solutions of nonlinear evolution equations. The \((3+1)\)-dimensional modified KdV-ZK equation and Whitham-Broer-Kaup equation are chosen to illustrate the application of the elliptic equation method. Consequently, new elliptic function solutions of rational forms are derived that are not obtained by the previously known methods.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
33E05	Elliptic functions and integrals
35C05	Solutions to PDEs in closed form

Software:

RATH; RAEEM; MACSYMA

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