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.
Highlights
It is well observed that almost every natural phenomena is nonlinear and mathematically which appears in the form of nonlinear evolution equations (NLEEs).The studies of NLEEs, a special type of nonlinear partial
Dierential equations (NPDEs), becomes one of the most exciting and extremely active areas of research and investigation because several problems in various scientic and engineering elds, such as solid state physics, chemical physics, plasma physics, optics, biology, chemical kinematics, geochemistry, uid mechanics and hydrodynamics are frequently describe by NLEEs
This paper is organized as follows: In Section 2, we will review briey the generalized (G0 /G)-expansion method.In Section 3, we present the application of the methods to Eq (1) and Eq (2)and the obtained solutions
Summary
It is well observed that almost every natural phenomena is nonlinear and mathematically which appears in the form of nonlinear evolution equations (NLEEs).The studies of NLEEs, a special type of nonlinear partial. No one studied the solutions to the aforesaid equations through the generalized (G0 /G)-expansion method. This paper is organized as follows: In Section 2, we will review briey the generalized (G0 /G)-expansion method.In Section 3, we present the application of the methods to Eq (1) and Eq (2)and the obtained solutions. Where u = u(x, t) is an unknown function, P is a polynomial in u(x, t) and its partial derivatives in which the highest order derivatives and the nonlinear terms are involved.The main steps of the generalized (G0 /G)expansion method are as follows: Step 1: We suppose that the combination of real variables x and t by a variable ξ as follows:. . ., N ), d and c into (6) yields the comprehensive and newly produced exact traveling wave solutions of the nonlinear partial dierential equation (3).
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