Abstract:
In this work, we focus on a general procedure for finding exact travelling wave
solutions for evolution equations with polynomial nonlinearites. Mathematically, looking for travelling wave solutions is asking the question whether a
given PDE has solutions invariant under a Galilean transformation; in such
a case, it can be reduced to an ODE. We discuss the existence of travelling
wave solutions by using phase plane analysis. We show that popular methods
such as the tanh-method, G0/G-method and many more are special cases of
the presented approach. Analytical solutions to several examples of nonlinear equations are illustrated. In the application, we use the Maple program
to compute solutions to nonlinear systems of equations.
