JAMP  Vol.5 No.9 , September 2017
Exact Solutions to the Boussinesq-Burgers Equations
Abstract: A nonlinear transformation from the solution of a linear equation to the solution of the Boussinesq-Burgers equations is derived by using the simplified homogeneous balance method. Based on the nonlinear transformation and various given solutions of the linear equation, various exact solutions, including solitary wave solutions, rational solutions, the solutions containing hyperbolic functions and the solutions containing trigonometric functions, of the Boussinesq-Burgers equations are obtained.
Cite this paper: Li, X. , Li, B. , Chen, J. and Wang, M. (2017) Exact Solutions to the Boussinesq-Burgers Equations. Journal of Applied Mathematics and Physics, 5, 1720-1724. doi: 10.4236/jamp.2017.59145.

[1]   Li, X.M. and Chen, A.H. (2005) Darboux Transformation and Multi-Solton Solutions of Boussinesq-Burgers Equation. Physics Letters A, 342, 413-420.

[2]   Khalfallah, M. (2009) Exact Travelling Wave Solutions of Boussinesq-Burgers Equation. Mathematical and Computer Modelling, 49, 666-671.

[3]   Rady, A.S.A. and Khalfallah, M. (2010) On Soliton Solutions for Boussibesq-Burgers Equations. Communication in Nonlinear Science and Numerical Simulation, 15, 886-894.

[4]   Wang, P., Tian, B., Liu, W.J., Lu, X. and Jiang, Y. (2011) Backlund Transformation and Multi-Soliton Solutions for the Boussinesq-Burgers Equations from Shallow Water Waves. Applied Mathematics and Computation, 218, 1726-1734.

[5]   Ravi, L.K., Ray, S.S. and Sahoo, S. (2017) New Exact Solutions of Coupled Boussinesq-Burgers Equations by Exp-Function Method. Journal of Ocean Engineering and Science, 2, 34-36.

[6]   Li, Q., Xia, T.C. and Chen, D.Y. (2017) 2N+1-Soliton Solutions of Boussinesq-Burgers Equation. Communications in Mathematical Research, 33, 26-32.

[7]   Wang, M.L., Li, X.Z. and Zhang, J.L. (2014) Simplified Homogeneous Balance Method and Its Application to Whitham-Broer-Kaup Equations. Journal of Applied Mathematics and Physics, 2, 823-827.

[8]   Wang, M.L., Zhang, J.L. and Li, X.Z. (2016) Decay Mode Solutions to Cylindrical KP Equation. Applied Mathematics Letters, 62, 29-34.

[9]   Wang, M.L., Zhang, J.L. and Li, X.Z. (2017) N-Dimensional Auto-Bäcklund Transformation and Exact Solutions to n-Dimensional Burgers System. Applied Mathematics Letters, 63, 46-52.