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. | |