Abstract
In this article, a technique namely Tanh method is applied to obtain some traveling wave solutions for Kupershmidt equation, and by using LADM we obtain an approximate solution to timefractional Kupershmidt equation.A comparison between the traveling wave solution (exact solution) and the approximate one of equation under study, indicate that Laplace Adomian Decomposition Method (LADM) is highly accurate and can be considered a very useful and valuable method.
Highlights
The study of nonlinear evolution equations have attracted attention of many mathematicians and physicists
To investigate the traveling wave solutions [10, 18], we propose in this work the Tanh method, because it is a powerful technique to search for traveling waves coming out from one-dimensional nonlinear wave and evolution equations
Some evolution problems do not admit the traveling wave solutions, due to that, we propose a semianalytical method called Laplace Adomian Decomposition Method (LADM), it is a combination of the Adomian Decomposition Method (ADM) and Laplace transforms
Summary
The study of nonlinear evolution equations have attracted attention of many mathematicians and physicists. The ADM is a method to solve ordinary and nonlinear differential equations Using this method is possible to express analytic solutions in terms of a series. Inverting and applying the highest order differential operator that is contained in the linear part of the equation, it is possible to express the solution in terms of the rest of the equation affected by the inverse operator. At this point, the solution is proposed by means of a series with terms that will be determined and that give rise to the Adomian polynomials. All results and plots bellow are obtained by using Mathematica software
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