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Solitary Solutions to the Generalized Burgers Fisher Equation and the Generalized Burgers Huxley Equation by the Sine Cosine Method.


Affiliations
1 Department of Physics, Dhanamanjuri College of Science, Imphal 795 001, India
     

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In this paper, we obtain solitary solutions to two Nonlinear Evolution Equations(NLEEs ) namely Generalized Burgers Fisher Equation (GBFE ) and the Generalized Burgers Huxley Equation (GBHE ) by the sine cosine method. It is shown that the sine cosine method provides a straight forward and powerful tool for solving Nonlinear Evolution Equations in Mathematical Physics and other relevant interdisciplinary sciences.

Keywords

Solitary Solution, NLEEs, GBFE, GBHE, NLPDE, NLODE, Sine Cosine Method
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  • Ablowitz, M. J. and Clarkson, P. A.,1991, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform method, Cambridge Univ. Press, Cambridge.

  • Hirota, R.,2004, The direct method in Soliton Theory, Cambridge University Press, Cambridge.

  • Kim, J.,2007, “A numerical method for the Cahn – Hilliard equation with a variable mobility”, Commun. Nonlinear Sci. Numer. Simul. 12 ,1560 – 1571.

  • Biazar ,J and Mahmoodi, 2010, “Applications of Differential Transform method to the Generalized Burgers Huxley Equation”, Appl. Appl. Math. 5 (10), 1726 – 1740.

  • He, J. H. and Wu, X. H. , 2006, “Construction of Solitary Solutions and Compacton like Solution by Variational Iteration method”, Chaos, Solitons Fractals, 29(1) ,108 – 113.

  • Farlow, S. J., 1993, Partial Differential Equations for Scientists and Engineers, Dover Publications, New York, .

  • Feng, Z. S., 2002, “The First Integral method to study the Burgers Korteweg de Vries equation”, J. Phys. A. Math. Gen. 35 (2) , 343 – 349.

  • Ren, Y. J. and. Zhang, H. Q, 2006, “A Generalized F – expansion method to find abundant families of Jacobi elliptic function solutions of the (2 + 1) dimensional Nizhnic-Novikov- Veselov equation”, Chaos,Solitons Fractals, 27(4) , 959 – 979.

  • Adomian, G., 1994, Solving Frontier Problems of Physics: The Decomposition Method, Kulwer Academic Publishers, Boston.

  • Miura, M. R., 1978, Backlund Transformation, Springer Verlag .

  • Tang, M.Y., Wang, R.Q. and Jing, J. Z., 2002, “Solitary waves and Bifurcations of KdV like equations with higher order nonlinearity”, Sci. China Ser. A Math. 45, 1255 – 1267.

  • Fang, E. and Zhang, H. , 1998, “A note on the Homogeneous Balance method”, Phys. Lett. A 246 , 403 – 406.

  • He, J. H., 2005, “Application of Homotopy Perturbation method to Nonlinear Wave Equations”, Chaos, Solitons Fractals 26 , 695 – 700.

  • He, J. H., 2006, “New Interpretation of Homotopy Perturbation method”, Int. J. Mod. Phys. B 20, 2561 – 2568.

  • Liu, S., Fu, Z., Liu S. D. and Zhao, Q., 2001, “Jacobi Elliptic function expansion method and Periodic Wave solutions of Nonlinear wave equations”, Phys. Lett. A 289 , 69 – 74.

  • Fan, E. and Jhang, J., 2002, “Applications of the Jacobi Elliptic function method to special type of Nonlinear equations”, Phys. Lett. A 305 ,383 – 392.

  • Kudriashov, N. A., 1990, “Exact solutions of Generalized Kuramoto Shivashynki equation”, Phys. Lett. A 147 , 287 – 291.

  • Kudriashov, N. A. 1991, “On types of Nonlinear Non integrable equations with exact solutions, Phys. Lett. A 155 , 269 – 275.

  • He, J. H. and Abdou, M. A., 2007, “New Periodic Solutions for Nonlinear Evolution Equations using Exp- function method”, Chaos, Solitons Fractals 34 (5) , 1421 – 1429.

  • Raslan, K., 2009, “The Application of He’s Exp- function method for MKdV and Burgers Equations with variable coefficients”, IJNS 7(2) , 174 – 189.

  • Wadati, M., 1972, “The Exact Solution of MKdV equation”, J. Phys. Soc. Jpn. 32, 1681 -1687.

  • Malfliet, W., 1992, “Solitary wave solutions of Nonlinear wave equations, Am. J. Phys. 60(7) , 650 -654.

  • Malfliet, W. and Hereman, W., 1996, “The Tanh method I : Exact solutions of Nonlinear Evolution Equations and Wave equations”, Phys. Scr. 54, 563 – 568.

  • Malfliet, W., 2004, “Tanh method: A tool for solving certain classes of Nonlinear Evolution Equations and wave equations”, J. Comput. Appl. Math. 164 – 165 , 529 – 541.

  • Wazwaz, A. M., 2006, “The Tanh method for compact and non compact solutions for variants of KdV- Burgers equation”, Physica D, 213(2) , 147 – 151.

  • Jawad, A. J. M., Petkovic, M. D. and Biswas, A., 2010, “Soliton solutions of a few Nonlinear wave equations”, Appl. Math. Comput. 216(9), 2649 – 2658.

  • Khater, A. H., Malfliet, W., Callebaut, D. K. and Kamel, E. S., 2002, “The Tanh method, a simple transformation and exact analytical solutions for Nonlinear reaction diffusion equation”, Chaos, Solitons Fractals 14(3) ,513 - 522.

  • Fan, E. , 2000, “Extended tanh function method and its applications to nonlinear equations” , Phys. Lett. A 277(4) , 212 -218

  • Yoshufoglu, E. and Bekir, A., 2007, “On the Extended tanh method: Applications of Nonlinear equations” , IJNS 4(1) , 10 – 16.

  • Wazwaz, A.M., 2007, “The Extended tanh method for new soliton solutions for many forms of the fifth order KdV equations”, Appl. Math. Comput. 184, 1002 – 1014.

  • Zayed, E. M. E. and Abdul Rahaman ,H. M., 2010, “The Extended tanh method for finding travelling wave solutions of nonlinear partial differential equations” ,Nonlinear Science Letters A 1(2) , 193 – 200.

  • Wazwaz, A. M., 2004, “A sine cosine method for handling nonlinear wave equations”, Math. Comput. Modell. 40,499 - 508.

  • Wazwaz, A. M., 2004, “The sine cosine method for obtaining solutions with compact and non compact structures”, Appl. Math. Comput. 152(2), 559 – 576.

  • Ali, A. H. A., Soliman, A. A. and Raslan, K. R., 2007, “Soliton solutions for Nonlinear Partial Differential equations by cosine function method”, Phys. Lett. A 368, 299 – 304.

  • Yoshufoglu, E., Bekir, A. and Alp, M., 2008, “Periodic and solitary wave solutions of Kawahara and Modified Kawahara equations by sine cosine method”, Chaos, Solitons Fractals 37(4), 1193 -1197.

  • Ma, W. X. and Lee, J.H., 2009, “A Transformed Rational function method and exact solutions to the (3 + 1) dimensional Jimbo – Miwa equation”, Chaos, Solitons Fractals 42, 1356 -1363.

  • Behzadi, S.S., 2011, “Numerical solution for solving Burgers Fisher equation by using iterative methods”, MCA 16(2) ,443 – 455.

  • Taghizade ,N. and Akbari, M., 2011, “The solutions of some equations by Perturbation method”, Aust. J. Basic Appl. Sci. 5(2) , 222 – 229.

  • Kocacoban, D., Koc, A.B. , Kurnaz ,A. and Keskin, Y., 2011, “A better approximation to the solution of Burgers Fisher equation” , WCE Vol. 1, .

  • Tanoglu, G., 2006, “Hirota method for solving Reaction Diffusion equations with generalized nonlinearity”, IJNS 1(1) , 30 – 36.

  • Bataineh, A.S., Noorani ,M.J.M. and Hasim, I., 2009, “Analytical treatment of Generalized Burgers Huxley equation by Homtopy Analysis method”, BMMSS (2) 32(2) , 233 – 243.


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  • Solitary Solutions to the Generalized Burgers Fisher Equation and the Generalized Burgers Huxley Equation by the Sine Cosine Method.

Abstract Views: 642  |  PDF Views: 2

Authors

S Subhaschandra Singh
Department of Physics, Dhanamanjuri College of Science, Imphal 795 001, India

Abstract


In this paper, we obtain solitary solutions to two Nonlinear Evolution Equations(NLEEs ) namely Generalized Burgers Fisher Equation (GBFE ) and the Generalized Burgers Huxley Equation (GBHE ) by the sine cosine method. It is shown that the sine cosine method provides a straight forward and powerful tool for solving Nonlinear Evolution Equations in Mathematical Physics and other relevant interdisciplinary sciences.

Keywords


Solitary Solution, NLEEs, GBFE, GBHE, NLPDE, NLODE, Sine Cosine Method

References