Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods

  • Jalil Manafian Heris
  • Isa Zamanpour

Abstract

In this article, we establish exact travelling wave solutions of the symmetric regularized long wave (SRLW) by using analytical methods. The analytical methods are: the tanh-coth method and the sech^2 method which used to construct solitary wave solutions of nonlinear evolution equations. With the help of symbolic computation, we show that aforementioned methods provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Author Biography

Jalil Manafian Heris
Department mathematics, university ahar

References

R. Hirota, The Direct Method in Soliton Theory, Cambridge Univ. Press, 2004.

M.J. Ablowitz, P.A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, Cambridge:

Cambridge University Press, 1991.

A. M. Wazwaz, Travelling wave solutions for combined and double combined sine-cosine-Gordon

equations by the variable separated ODE method, Appl. Math. Comput, 177 (2006) 755-760.

M. Dehghan, J. Manafian, The solution of the variable coefficients fourth–order parabolic partial

differential equations by homotopy perturbation method, Z. Naturforsch, 64 (2009) 420-430.

M. Dehghan, J. Manafian, A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch, 65a (2010) 935-949.

M. Dehghan, J. Manafian, A. Saadatmandi, Solving nonlinear fractional partial differential equations

using the homotopy analysis method, Num. Meth. Partial Differential Eq. J, 26 (2010) 448-479.

J. H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech, 34 (1999) 699-708.

M. Dehghan, M. Tatari, Identifying an unknown function in a parabolic equation with overspecified

data via He’s variational iteration method, Chaos Solitons Fractals, 36 (2008) 157-166.

M. Dehghan, J. Manafian, A. Saadatmandi, Application of semi-analytic methods for the Fitzhugh-

Nagumo equation, which models the transmission of nerve impulses, Math. Meth. Appl. Sci, 33 (2010) 1384-1398.

M. Wang, X. Li, J. Zhang, The (G0 G )-expansion method and travelling wave solutions of nonlinear

evolution equations in mathematical physics, Phys. Lett. A, 372 (2008) 417-423.

J. Manafianheris, Exact Solutions of the BBM and mBBM Equations by the Generalized (G0 G )-expansion Method Equations, International Journal of Genetic Eng, 2 (2012) 28-32.

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

J. Manafian Heris, M. Lakestani, Solitary wave and periodic wave solutions for variants of the KdVBurger and the K(n,n)Burger equations by the generalized tanhcoth method, Communications in Numerical Analysis. 2013 (2013) 1-18.

X. H. Menga, W. J. Liua, H. W. Zhua, C. Y. Zhang, B. Tian, Multi-soliton solutions and a Backlund transformation for a generalized variable-coefficient higher-order nonlinear Schrodinger equation with symbolic computation, Phys. A, 387 (2008) 97-107.

X. Lu, H. W. Zhu, X. H. Meng, Z. C. Yang, B. Tian, Soliton solutions and a B¨acklund transformation for a generalized nonlinear Schr¨odinger equation with variable coefficients from optical fiber communications, J. Math. Anal. Appl, 336 (2007) 1305-1315.

J. Manafian Heris, M. Bagheri, Exact solutions for the modified KdV and the generalized KdV equations via Exp-function method, J. Math. Extension, 4 (2010) 77-98.

J. Manafian Heris, Isa Zamanpour, ANALYTICAL TREATMENT OF THE COUPLED HIGGS

EQUATION AND THE MACCARI SYSTEM VIA EXP-FUNCTION METHOD, Acta Universitatis Apulensis, 33 (2013) 203-216.

F. Xu, Application of Exp–function method to Symmetric Regularized Long Wave (SRLW) equation, Phsy Comput, 372 (2008) 252–257.

M. Dehghan, J. Manafian Heris, A. Saadatmandi, Application of the Exp-function method for solving a partial differential equation arising in biology and population genetics, Int. J. Num. Methods for Heat Fluid Flow, 21 (2011) 736-753.

M. Dehghan, J. Manafian Heris, A. Saadatmandi, Analytical treatment of some partial differential equations arising in mathematical physics by using the Exp-function method, Int. J. Modern Phys. B, 25 (2011) 2965-2981.

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

W. Malfliet, Willy Hereman, The tanh method: II. Perturbation technique for conservative systems,

Phys. Scr, 54 (1996) 569-575.

A.M. Wazwaz, The extended tanh method for new solitons solutions for many forms of the fifth–order KdV equations, Appl. Math. Comput, 184 (2007) 1002-1014.

A.M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equation, Appl. Math. Comput, 169 (2005) 321-338.

Published
2014-02-22
How to Cite
Manafian Heris, J., & Zamanpour, I. (2014). Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods. Statistics, Optimization & Information Computing, 2(1), 47-55. https://doi.org/10.19139/soic.v2i1.69
Section
Research Articles