Periodic, kink and bell shape wave solutions to the Caudrey-Dodd-Gibbon (CDG) equation and the Lax equation

Year 2020, , 216 - 232, 30.12.2020

Md. Khorshed Alam

https://doi.org/10.31197/atnaa.762574

Abstract

This paper addresses the implementation of the new generalized ((G')⁄G)-expansion method to the Caudrey-Dodd-Gibbon (CDG) equation and the Lax equation which are two special case of the fifth-order KdV (fKdV) equation. The method work well to derive a new variety of travelling wave solutions with distinct physical structures such as soliton, singular soliton, kink, singular kink, bell-shaped soltion, anti-bell-shaped soliton, periodic, exact periodic and bell type solitary wave solutions. Solutions provided by this method are numerous comparing to other methods. To understand the physical aspects and importance of the method, solutions have been graphically simulated. Our results unquestionably disclose that new generalized ((G')⁄G)-expansion method is incredibly influential mathematical tool to work out new solutions of various types of nonlinear partial differential equations arises in the fields of applied sciences and engineering.

Keywords

Caudrey-Dodd-Gibbon (CDG) equation, Lax equation, New generalized ((G')⁄G)-expansion method

References

• Weiss, J., Tabor, M. and Carnevale, G. 1983. The Painleve property for partial differential equations. J. Math. Phys. 24: 522-526.
• Ablowitz, M.J. and Clarkson, P.A. 1991. Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge. 516 pp.
• Beals, R. and Coifman, R.R. 1984. Scattering and inverse scattering for 1st order system, Commun. Pure. Appl. Math.37: 39-90. Matveev, V.B. and Salle, M.A. 1991. Darboux Transformations and Solitons. Springer-Verlag, Berlin.120 pp.
• Cai, H., Jing, S., De-Chen, T. and Nian-Nin, H. 2002. Darboux Transformation Method for Solving the Sine-Gordon Equation in a Laboratory Reference. Chin. Phys. Lett. 19(7): 908-911.