Exact solutions to some nonlinear PDEs, travelling profiles method

N. Benhamidouche, University of M'sila, M'sila, Algeria

E. J. Qualitative Theory of Diff. Equ., No. 15. (2008), pp. 1-7.

Abstract: We suggest finding exact solutions of equation:

\begin{equation*}
\frac{\partial u}{\partial t}=(\frac{\partial ^{m}}{\partial x^{m}}u)^{p},
t\geq 0, x\in \mathbb{R}, m, p\in \mathbb{N}, p>1,
\end{equation*}

by a new method that we call the travelling profiles method. This method allows us to find several forms of exact solutions including the classical forms such as travelling-wave and self-similar solutions.

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