New solitary wave in shallow water,plasma and ion acoustic plasma via the GZK-BBM equation and the RLW equation

This work obtains the disguise version of exact solitary wave solutions of the generalized(2+1)-dimensk>nal Zakharov-Kuznetsov-Benjamin-Bona-Mahony and the regu­larized long wave equation with some free parameters via modified simple equation method(MSE).Usually the method does not give any solution if the balance number is more than one,but we apply MSE method successfully in different way to carry out the solutions of nonlinear evolution equation with balance number two.Finally some graphical results of the velocity profiles are presented for different values of the material constants.It is shown that this method,without help of any symbolic computation,provide a straightforward and powerful mathematical tool for solving nonlinear evolution equation.

Novel solitary wave solution in shallow water and ion acoustic plasma waves in-terms of two nonlinear models via MSE method

By using modified simple equation method,we study the generalized RLW equation and symmetric RLW equation,the subsistence of solitary wave,periodic cusp wave,periodic bell wave solutions are obtained.We establish some conditions on the parameters for which the obtained solutions are dark or bright soliton.The proficiency of the methods for constructing exact solutions has been established.Finally,the variety of structure and graphical representation makes the dynamics of the equations visible and provides the mathematical foundation in shallow water,plasma and ion acoustic plasma waves.