The (ω/ g )-expansion method and its application to Vakhnenko equation

Abstract

This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the (ω/g)-expansion method, which can be thought of as the generalization of (G /G)-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.

Application of the -expansion method to Kawahara type equations using symbolic computation

“…As in the previous case, if we compare our results with Yusufoglu and Bekir's results [37] and Wazwaz's results [38], then we see that the results (5.5) and (5.8) in [37] are special cases of our results (20), (21), (23), (24) and so are the results (29)- (32) in [39]. Besides, the rational function solutions (22) are new and not obtained by the methods in [37,38].…”

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2Sirisubtawee1, Koonprasert2 2018Advances in Mathematical Physics440210View full textAdd to dashboardCite

“…The modified method can be thought as the generalization of the well-known ( / )-expansion method introduced in [37] with the special functions and including the case of = and = 2 . In particular, Wen-An et al [35] applied the modified method, i.e., the ( / 2 )-expansion method, to find the traveling wave solutions of the Vakhnenko equation. Zhouzheng [38] applied the ( / 2 )-expansion method to obtain the exact solutions of the modified Benjamin-Bona-Mahony (MBBM) and Ostrovsky-Benjamin-Bona-Mahony (OBBM) equations.…”

“…For example, Chen [34] gave the application of the ( / 2 )-expansion method for seeking exact solutions of the coupled nonlinear Klein-Gordon equation. Wen-An et al [35] demonstrated the use of the ( / )-expansion method for finding traveling wave solutions of a nonlinear evolution equation. Zayed and 2…”

Expanded (G/G2) Expansion Method to Solve Separated Variables for the 2+1-Dimensional NNV Equation

“…Li proposed an expansion method in [20] to solve the new traveling wave solution for the Vakhnenko equation. However, for a large number of nonlinear systems, it is difficult to fully describe only the traveling wave solution, and it will inevitably lose other solutions with a rich structure.…”