Soliton solutions of some nlees with time dependent coefficients where the velocity vt is given by eq 4 and it should be noted that the soliton solution eq 6 exists under the condition tt0figure 1 shows the numerical simulation. This paper exhibits the application of integrability aspects to a couple of nonlinear evolution equations these are semi inverse variational principle and the rational sine cosine method these are applied to extract solutions of boiti leon manna pempinelli equation and breaking soliton equation soliton and other solutions will be . The construction of exact traveling wave solutions of nonlinear evolution equations nees is one of the most important and essential tasks in nonlinear science since these solutions will very well describe various natural phenomena such as vibrations solitons and propagation with a finite speed. Abstract in this paper we obtain exact soliton solutions of the modified kdv equation inhomogeneous nonlinear schrdinger equation and gm n equation with variable coefficients using solitary wave ansatzthe constraint conditions among the time dependent coefficients turn out as necessary conditions for the solitons to exist. Emphasis is given to the multi dimensional problems arising and includes inverse scattering in multi dimensions integrable nonlinear evolution equations in multi dimensions and the method thus this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory
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