JAMP  Vol.2 No.8 , July 2014
Simplified Homogeneous Balance Method and Its Applications to the Whitham-Broer-Kaup Model Equations
Abstract: A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation. 
Cite this paper: Wang, M. and Li, X. (2014) Simplified Homogeneous Balance Method and Its Applications to the Whitham-Broer-Kaup Model Equations. Journal of Applied Mathematics and Physics, 2, 823-827. doi: 10.4236/jamp.2014.28091.

[1]   Whitham, G.B. (1967) Variational Methods and Applications to Water Waves. Proceedings of the Royal Society A, 299, 6-25.

[2]   Broer, L.J. (1975) Approximate Equations for Long Water Waves. Applied Scientific Research, 31, 377-395.

[3]   Kaup, D.J. (1975) A Higher-Order Water-Wave Equation and the Method for Solving It. Progress of Theoretical Physics, 54, 396-408.

[4]   Kupershmidt, B.A. (1985) Mathematics of Dispersive Waves. Communications in Mathematical Physics, 99, 51-73.

[5]   Fan, E. and Zhang, H. (1998) Backlund Transformation and Exact Solutions for Whitham-Broer-Kaup Equations in Shallow Water. Applied Mathematics and Mechanics, 19, 713-716.

[6]   Wazwaz, A.M. (2013) Multiple Soliton Solutions for the Whitham-Broer-Kaup Model in Shallow Water Small-Amplitude Regime. Physica Scripta, 88.

[7]   Wang , M.L. (1995) Solitary Wave Solutions for Variant Boussinesq Equations. Physics Letters A, 199, 169-172.

[8]   Wang, M.L. (1996) Exact Solutions for a Compound KdV-Burgers Equation. Physics Letters A, 213, 279-287.

[9]   Wang , M.L., Zhou, Y.B. and Li, Z.B. (1996) Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Equations in Mathematical Physics. Physics Letters A, 216, 67-75.

[10]   Calogero, F. (1991) Springer Series in Nonlinear Dynamics. Zakharov, V.E., Ed., Springer, Berlin, 1-62.