Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33093
New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
Abstract:
In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.
Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082135
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1488References:
[1] J.H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Non-linear Mech. 34(4) (1999) 699- 708.
[2] M.T. Darvishi, F. Khani, A.A. Soliman, The numerical simulation for stiff systems of ordinary differential equations, Comput. Math. Appl. 54(7-8) (2007) 1055-1063.
[3] M.T. Darvishi, F. Khani, Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations, Chaos, Solitons and Fractals 39 (2009) 2484-2490.
[4] J.H. He, New interpretation of homotopy perturbation method, Int. J. Mod. Phys. B 20(18) (2006) 2561-2568.
[5] J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals 26(3) (2005) 695-700.
[6] J.H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul. 6(2) (2005) 207-208.
[7] M.T. Darvishi, F. Khani, Application of He-s homotopy perturbation method to stiff systems of ordinary differential equations, Zeitschrift fur Naturforschung A, 63a (1-2) (2008) 19-23.
[8] M.T. Darvishi, F. Khani, S. Hamedi-Nezhad, S.-W. Ryu, New modification of the HPM for numerical solutions of the sine-Gordon and coupled sine- Gordon equations, Int. J. Comput. Math. 87(4) (2010) 908-919.
[9] J.H. He, Bookkeeping parameter in perturbation methods, Int. J. Nonlin. Sci. Numer. Simul. 2 (2001) 257-264.
[10] M.T. Darvishi, A. Karami, B.-C. Shin, Application of He-s parameterexpansion method for oscillators with smooth odd nonlinearities, Phys. Lett. A 372(33) (2008) 5381-5384.
[11] B.-C. Shin, M.T. Darvishi, A. Karami, Application of He-s parameterexpansion method to a nonlinear self-excited oscillator system, Int. J. Nonlin. Sci. Num. Simul. 10(1) (2009) 137-143.
[12] M.T. Darvishi, Preconditioning and domain decomposition schemes to solve PDEs, Int-l J. of Pure and Applied Math. 1(4) (2004) 419-439.
[13] M.T. Darvishi, S. Kheybari and F. Khani, A numerical solution of the Korteweg-de Vries equation by pseudospectral method using Darvishi-s preconditionings, Appl. Math. Comput. 182(1) (2006) 98-105.
[14] M.T. Darvishi, M. Javidi, A numerical solution of Burgers- equation by pseudospectral method and Darvishi-s preconditioning, Appl. Math. Comput. 173(1) (2006) 421-429.
[15] M.T. Darvishi, F. Khani and S. Kheybari, Spectral collocation solution of a generalized Hirota-Satsuma KdV equation, Int. J. Comput. Math. 84(4) (2007) 541-551.
[16] M.T. Darvishi, F. Khani, S. Kheybari, Spectral collocation method and Darvishi-s preconditionings to solve the generalized Burgers-Huxley equation, Commun., Nonlinear Sci. Numer. Simul. 13(10) (2008) 2091- 2103.
[17] S.J. Liao, An explicit, totally analytic approximate solution for Blasius viscous flow problems, Int. J. Non-Linear Mech. 34 (1999) 759-778.
[18] S.J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, 2003.
[19] S.J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput. 147 (2004) 499-513.
[20] S.J. Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. Heat Mass Transfer 48 (2005) 2529- 2539.
[21] S.J. Liao, A general approach to get series solution of non-similarity boundary-layer flows, Commun. Nonlinear Sci. Numer. Simul. 14(5) (2009) 2144-2159.
[22] M.T. Darvishi, F. Khani, A series solution of the foam drainage equation, Comput. Math. Appl. 58 (2009) 360-368.
[23] J.H. He, M.A. Abdou, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals 34 (2007) 1421-1429.
[24] J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals, 30(3) (2006) 700-708.
[25] J.H. He, X.H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons and Fractals, 29 (2006) 108-113.
[26] F. Khani, S. Hamedi-Nezhad, M.T. Darvishi, S.-W. Ryu, New solitary wave and periodic solutions of the foam drainage equation using the Expfunction method, Nonlin. Anal.: Real World Appl. 10 (2009) 1904-1911.
[27] B.-C. Shin, M.T. Darvishi, A. Barati, Some exact and new solutions of the Nizhnik-Novikov-Vesselov equation using the Exp-function method, Comput. Math. Appl. 58(11/12) (2009) 2147-2151.
[28] X.H. Wu, J.H. He, Exp-function method and its application to nonlinear equations, Chaos, Solitons and Fractals 38(3) (2008) 903-910.
[29] A.M. Wazwaz, New solutions of distinct physical structures to highdimensional nonlinear evolution equations, Appl. Math. Comput., 196 (2008) 363-370.
[30] A.M. Wazwaz, The (2+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions, Zeitschrift fur Naturforschung A 65a, (2010) 173-181.
[31] A.M. Wazwaz, Multiple-soliton solutions for the Calogero- Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations, Appl. Math. Comput., 203 (2008) 592-597.
[32] Z.-H. Zhao, Z. Dai, S. Han, The EHTA for nonlinear evolution equations, Appl. Math. Comput., (in press), doi:10.1016/j.amc.2010.09.069.