J. Nonl. Evol. Equ. Appl. 2013 (5), pp. 55-65, published on August 20, 2014:

New Multi-order exact solutions for a class of nonlinear evolution equations

B. Bagchi, S. Das

Department of Applied Mathematics, University of Calcutta
92 Acharya Prafulla Chandra Road, Kolkata-700009, India

A. Ganguly

Department of Mathematics, Indian Institute of Technology, Kharagpur
Kharagpur-721302, India

Received on August 21, 2012; Revised version December 4, 2012
Accepted on December 8, 2012

Communicated by Ti-Jun Xiao

Abstract.  In this article multi-order exact solutions of a generalized shallow water wave equation are sought in addition to those belonging to a class of nonlinear systems such as the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. A modified version of a generalized Lame equation is employed within a perturbative framework and the solutions are identified order byorder in terms of Jacobi elliptic functions. The multi-order exact solutions turn out to be 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 the previous results reported in the literature are recovered.
Keywords: Travelling waves; Lamé equation; Lamé function; Jacobi elliptic function; Elliptic integral function.
2010 Mathematics Subject Classification:   34A34, 34G20, 47J35.

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