Abstract
The Exp-function method is generalized to construct N-soliton solutions of a new generalization of the associated Camassa-Holm equation. As a result, one-soliton, two-soliton, and three-soliton solutions are obtained, from which the uniform formulae of N-soliton solutions are derived. It is shown that the Exp-function method may provide us with a straightforward, effective, and alternative mathematical tool for generating N-soliton solutions of nonlinear evolution equations in mathematical physics.
Highlights
The investigation of the traveling wave solutions to nonlinear evolution equations (NLEEs) plays an important role in mathematical physics
A lot of physical models have supported a wide variety of solitary wave solutions
Much efforts have been spent on this task and many significant methods have been established such as inverse scattering transform [1], Backlund and Darboux transform [2], Hirota bilinear method [3], homogeneous balance method [4], Jacobi elliptic function method [5], tanh-function method [6], Exp-function method [7], simple equation method [8], F-expansion method [9, 10], improved F-expansion method [11], and extended F-expansion method [12]
Summary
The investigation of the traveling wave solutions to nonlinear evolution equations (NLEEs) plays an important role in mathematical physics. We study a new generalization of the associated Camassa-Holm equation. Where k is a nonzero real constant, was derived as a model for shallow water waves by Camassa and Holm in 1993 [13]. This equation is integrable with the following Lax pair: ψxx. (1) is transformed into the following associated Camassa-Holm (ACH) equation: ut + 2k3ux + 4k2uut + 2k2ux∂x−1ut − k2uxxt = 0. We would like to generalize the Exp-function method for constructing N-soliton solutions of ACH-KdV equation (6).
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