Travelling wave solutions to nonlinear evolution and wave equations

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Abstract
We have studied a series of (ansatze) ordinary differential equations of the first order, which correspond to the travelling (and/or solitary) wave solutions of some nonlinear partial differential equations. We have investigated the conditions, under which the nonlinear partial differential equations have certain kinds of travelling (and/or solitary) wave solutions. As a consequence of applications, we can take the trial procedures to obtain the travelling wave solutions, which is a very efficient method for solving several classes of nonlinear partial differential equations.