Exact solutions of \(\phi^4\) equation using Lie symmetry approach along with the simplest equation and exp-function methods. (English) Zbl 1257.35075

Summary: This paper obtains the exact solutions of the \(\phi^4\) equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.


35G20 Nonlinear higher-order PDEs
35C07 Traveling wave solutions
35B06 Symmetries, invariants, etc. in context of PDEs
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