Multi-Order Exact Solutions for a generalized shallow water wave equation and other nonlinear PDEs

Details Multi-Order Exact Solutions for a generalized shallow water wave equation and other nonlinear PDEs Multi-Order Exact Solutions for a generalized shallow water wave equation and other nonlinear PDEs

2011-11-20

arxiv.org/abs/1111.4644v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, 5 figs

Scientific paper

We seek multi-order exact solutions of a generalized shallow water wave equation along with those corresponding to a class of nonlinear systems described by the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. We employ a modified version of a generalized Lame equation and subject it to a perturbative treatment identifying the solutions order by order in terms of Jacobi elliptic functions. Our solutions are new and hold the key feature that they are expressible in terms of an auxiliary function f in a generic way. For appropriate choices of f we recover the previous results reported in the literature.

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