Abstract
In manuscript, with the help of the Wolfram Mathematica 9, we employ the modified exponential function method in obtaining some new soliton solutions to the ill-posed Boussinesq equation arising in nonlinear media. Results obtained with use of technique, and also, surfaces for soliton solutions are given. We also plot the 3D and 2D of each solution obtained in this study by using the same program in the Wolfram Mathematica 9.
Highlights
For some past decades explorations for the search of the new solutions to non-linear evolution equations (NLEEs) have attracted the attention of many scholars
Attention from different researchers has been paid to this area in searching for new solutions to the different class of NLEEs where various powerful method are formulated such as the generalized and improved G / G -expansion method [1], the Jacobi elliptic-function method [2], the modified simple equation method [3,4], the sine-Gordon expansion method [5,6,7], the extended tanh method [8], the improved Bernoulli sub-equation function method [9], the rational sine-cosine method [10], the RicattiBernoulli sub-ODE method [11], the Homotopy perturbation method [12] and so on
It is very important to look for some new solutions to this equation as it plays a vital roles in the field of applied mathematics
Summary
For some past decades explorations for the search of the new solutions to non-linear evolution equations (NLEEs) have attracted the attention of many scholars. Attention from different researchers has been paid to this area in searching for new solutions to the different class of NLEEs where various powerful method are formulated such as the generalized and improved G / G -expansion method [1], the Jacobi elliptic-function method [2], the modified simple equation method [3,4], the sine-Gordon expansion method [5,6,7], the extended tanh method [8], the improved Bernoulli sub-equation function method [9], the rational sine-cosine method [10], the RicattiBernoulli sub-ODE method [11], the Homotopy perturbation method [12] and so on. Some analytical methods for obtaining the solutions of ill-posed Boussinesq equation have been designed by different scientists, this include the solitary wave ansatz method and the Bernoulli subOde [18], the exp function method [19], the Adomian decomposition method [20] etc
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