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An Analytic Solution of Benjamin-Ono Equation by Functional Variable Method (FVM): Graphical Approaches on Wave Speed

Authors: Md. Monirul Islam; Md. Robiul Islam;

An Analytic Solution of Benjamin-Ono Equation by Functional Variable Method (FVM): Graphical Approaches on Wave Speed

Abstract

{"references": ["Bleecker, D., & Csordas, G. (1992). Basic partial differential equations. CRC Press", "Farlow, S. J. (1993). Partial differential equations for scientists and engineers. Courier Corporation", "John F.(1982). Partial Differential Equations, Springer-Verlag, New York", "Lam, L. (2000). Nonlinear Physics for Beginners", "Logan, J. D. (2008). An introduction to nonlinear partial differential equations (Vol. 89). John Wiley & Sons", "Wazwaz, A. M. (2002). Partial differential equations. CRC Press", "Hereman, W. (2009). Shallow water waves and solitary waves, Encyclopedia of Complexity and Systems Science, Ed.: RA Meyers", "Wazwaz, A. M. (2004). A sine-cosine method for handlingnonlinear wave equations. Mathematical and Computer modelling, 40(5-6), 499-508", "Malfliet, W., & Hereman, W. (1996). The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Physica Scripta, 54(6), 563.", "Alquran, M., Al-Khaled, K., & Ananbeh, H. (2011). New soliton solutions for systems of nonlinear evolution equations by the rational sine-cosine method. Studies in Mathematical Sciences, 3(1), 1-9."]}

In mathematical physics numerous methods has been applied for finding exact solutions of various nonlinear partial differential equations (NLPDEs). A very powerful solution method is the Functional Variable Method (FVM). In this paper, we discuss the validity & advantages of this method in the Benjamin-Ono equation and achieve graphical representation for different parameters. The Benjamin-Ono equation is the non K-dv type equation and we solve the non K-dv type equation in this paper. By using this useful method, it is shown that the FVM is effective and general than the other method. We presented the graphical representation of the soliton solutions for various wave speed.

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Keywords

Functional variable method; travelling wave; BO equation

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