Abstract
A generalized and improved(G′/G)-expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.
Highlights
The world around us is inherently nonlinear, and nonlinear evolution equations NLEEs are widely used as models to describe the complex physical phenomena
Many researchers who are interested in the nonlinear physical phenomena investigated exact solutions of NLEEs
We propose a generalized and improved G /G -expansion method for solving NLEEs in mathematical physics and engineering
Summary
The world around us is inherently nonlinear, and nonlinear evolution equations NLEEs are widely used as models to describe the complex physical phenomena. Wang et al 24 introduced a widely used straightforward method called the G /G -expansion method for obtaining the travelling wave solutions of various NLEEs, Mathematical Problems in Engineering where G ξ satisfies the second-order linear ordinary differential equation ODE G λG μG 0, and λ and μ are arbitrary constants. G /G i bi G /G i−1 σ 1 1/μ G /G 2} and obtained new travelling wave solutions of the Whitham-Broer-Kaup-like equation and couple Hirota-Satsuma KdV equations Applying this extended method Zayed and Al-Joudi constructed the traveling wave solutions of some nonlinear evolution equations. Zayed and Gepreel 34 employed the improved G /G -expansion method to Konopelchenko-Dubrovsky equation, Karsten-Krasil’ Shchik equation, Whitham-Broer-Kaup equation, and the fifth-order KdV equations to construct traveling wave solutions. ±m , d and V into 2.4 , we obtain more general type and new exact traveling wave solutions of the nonlinear evolution equation 2.1 Since the general solution of 2.5 is well known for us, substituting the values of an n 0, ±1, ±2, ±3, . . . , ±m , d and V into 2.4 , we obtain more general type and new exact traveling wave solutions of the nonlinear evolution equation 2.1
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