The extended homogeneous balance method and exact solutions of the Maccari system

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

The extended homogeneous balance method is used to construct exact traveling wave solutions of the Maccari system, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Maccari system equation are successfully obtained.

Keywords


[1] M.L. Wang. Solitrary wave solution for variant Boussinesq equation. Phys. Lett. A, 199, (1995)
169-172.
[2] M.L. Wang. Applicatian of homogeneous balance method to exact solutions of nonlinear equation
in mathematical physics. Phys. Lett. A, 216, (1996) 67-75.
[3] M. Khalfallah. New exact travelling wave solutions of the (3+1) dimensional KadomtsevPetviashvili
(KP) equation. Commun. Nonlinear Sci. Numer. Simul., 14, (2009) 1169-1175.
[4] M. Eslami, B. Fathi vajargah and M. Mirzazadeh. Exact solutions of modified ZakharovKuznetsov
equation by the homogeneous balance method. Ain Shams Engineering Journal,
5, (2014) 221-225.
[5] W. Malfliet. Solitary wave solutions of nonlinear wave equations, Am. J. Phys, 60(7), (1992)
650-654.
[6] W. Malfliet and W. Hereman. The tanh method: I. Exact solutions of nonlinear evolution and
wave equations, Phys. Scripta, 54, (1996) 563-568.
[7] W. Malfliet and W. Hereman. The tanh method: II. Perturbation technique for conservative
systems, Phys. Scripta, 54, (1996) 569-575.
[8] S.K. Liu, Z. Fu, S.D. Liu and Q. Zhao. Jacobi elliptic function method and periodic wave
solutions of nonlinear wave equations, Phys. Lett. A, 289, (2001) 69-74.
[9] Z. Feng. The first integral method to study the Burgers-Korteweg-de Vries equation, J. Phys.
A, 35(2), (2002) 343-349.
[10] Z. Feng and X.H. Wang. The first integral method to the two-dimensional Burgers-KdV equation,
Phys. Lett. A, 308, (2002) 173-178.
[11] Z. Feng and G. Chen. Solitary wave solutions of the compound Burgers-Korteweg-de Vries
equation, Physica A, 352, (2005) 419-435.
[12] X.Q. Zhao and D.B. Tang. A new note on a homogeneous balance method. Phys. Lett. A, 297,
(2002) 59-67.
[13] A. Bekir. New exact travelling wave solutions of some complex nonlinear equations. Commun.
Nonlinear. Sci. Numer. Simulat., 14, (2009) 1069-1077.
[14] C.M. Khalique. Exact solutions and conservation laws of a coupled integrable dispersionless
system. Filomat, 26(5), (2012) 957-964.
[15] Bouthina Ahmed, Anjan Biswas, E. V. Krishnan and Sachin Kumar, Solitons and other solutions
to the genereralized Maccari system. Romanian Reports in Physics, 65(4), (2013) 1138-1154.