Traveling Wave Solution of (2+1) Dimensional Boussinesq Equation by Bernoulli Sub-ODE Method

Abstract:

In this paper, we derive exact traveling wave soluti-ons of (2+1) dimensional Boussinesq equation by the known (G’/G) expansion method and a proposed Bernoulli sub-ODE method. We also make a comparison between the two method.

• Periodical: Advanced Materials Research (Volumes 403-408)
• Pages: 202-206
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.403-408.202
• Online since: November 2011
• Authors: Qing Hua Feng, Tong Bo Liu
• Keywords: (2+1) Dimensional Boussinesq Equation, (G’/G) Expansion Method, Bernoulli Sub-ODE Method, Traveling Wave Solutions

References

[1] M. Wang, Solitary wave solutions for variant Boussinesq equations, Phys. Lett. A 199 (1995) 169-172.J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, p.68–73.

DOI: 10.1016/0375-9601(95)00092-h

[2] E.M.E. Zayed, H.A. Zedan, K.A. Gepreel, On the solitary, . wave solutions for nonlinear Hirota-Satsuma coupled KdV equations, Chaos, Solitons and Fractals 22 (2004) 285-303.

DOI: 10.1016/j.chaos.2003.12.045

[3] L. Yang, J. Liu, K. Yang, Exact solutions of nonlinear PDE nonlinear transformations and reduction of nonlinear PDE to a quadrature, Phys. Lett. A 278 (2001) 267-270.

DOI: 10.1016/s0375-9601(00)00778-7

[4] E.M.E. Zayed, H.A. Zedan, K.A. Gepreel, Group analysis. and mod- ified tanh-function to find the invariant solutions and soliton solution for nonlinear Euler equations, Int. J. Nonlinear Sci. Numer. Simul. 5 (2004) 221-234.

DOI: 10.1515/ijnsns.2004.5.3.221

[5] M. Inc, D.J. Evans, On traveling wave solutions of some nonlinear evolution equations, Int. J. Comput. Math. 81 (2004) 191-202.

[6] M.A. Abdou, The extended tanh-method and its applications for solving nonlinear physical models, Appl. Math. Comput. 190 (2007) 988-996.

DOI: 10.1016/j.amc.2007.01.070

[7] E.G. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000) 212-218.

DOI: 10.1016/s0375-9601(00)00725-8

[8] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60 (1992) 650-654.

DOI: 10.1119/1.17120

[9] J.L. Hu, A new method of exact traveling wave solution for coupled nonlinear differential equations, Phys. Lett. A 322 (2004) 211-216.

[10] M.J. Ablowitz, P.A. Clarkson, Solitons, Non-linear Evolution Equations and Inverse Scattering Transform, Cambridge University Press, Cambridge, (1991).

[11] M.R. Miura, Backlund Transformation, Springer-Verlag, Berlin, (1978).

[12] C. Rogers, W.F. Shadwick, Backlund Transformations, Academic Press, New York, (1982).

[13] R. Hirota, Exact envelope soliton solutions of a nonlinear wave equation, J. Math. Phys. 14 (1973) 805-810.

DOI: 10.1063/1.1666399

[14] R. Hirota, J. Satsuma, Soliton solution of a coupled KdV equation, Phys. Lett. A 85 (1981) 407-408.