Abstract
In the paper, a auxiliary equation expansion method and its algorithm is proposed by studying a second order nonlinear ordinary differential equation with a four-degree term. The method is applied to the generalized Ben-ney-Luke (GBL) equation with any order. As a result, some new exact traveling wave solutions are obtained which singular solutions, triangular periodic wave solutions and jacobian elliptic function solutions .This algorithm can also be applied to other nonlinear wave equations in mathematical physics.
Highlights
The method is applied to the generalized Benney-Luke (GBL) equation with any order
Some new exact traveling wave solutions are obtained which singular solutions, triangular periodic wave solutions and jacobian elliptic function solutions. This algorithm can be applied to other nonlinear wave equations in mathematical physics
Nonlinear phenomena that appear in many areas of scientific fields such as solid state physics, plasma physics, fluid dynamics, mathematical biology and chemical kinetics can be modeled by partial differential equation
Summary
Nonlinear phenomena that appear in many areas of scientific fields such as solid state physics, plasma physics, fluid dynamics, mathematical biology and chemical kinetics can be modeled by partial differential equation. The investigation of exact traveling wave solution to nonlinear equations plays an important role in the study of nonlinear physical phenomena. Various methods for seeking traveling wave solutions to nonlinear partial differential equations are proposed such as inverse scattering transform method [1], BÄacklund and Darboux transform [2,3,4,5,6], Hirota method [7], Lie group method [8,9] and so on. We shall consider the following generalized Benney-Luke (GBL) equation [10]: tt a 2 b tt p t ( x ) p 1.
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