Some New Exact Traveling Wave Solutions for the Generalized Benney-Luke (GBL) Equation with Any Order

Affiliation(s)

Mathematics Department, Simao Teachers’ College, Pu’er, China.

Mathematics Department, Northwest University, Xi’an, China.

Mathematics Department, Simao Teachers’ College, Pu’er, China.

Mathematics Department, Northwest University, Xi’an, China.

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.

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.

Cite this paper

J. Wang, L. Wang and K. Yang, "Some New Exact Traveling Wave Solutions for the Generalized Benney-Luke (GBL) Equation with Any Order,"*Applied Mathematics*, Vol. 3 No. 4, 2012, pp. 309-314. doi: 10.4236/am.2012.34046.

J. Wang, L. Wang and K. Yang, "Some New Exact Traveling Wave Solutions for the Generalized Benney-Luke (GBL) Equation with Any Order,"

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