**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.

Communicated by P. Eloe.
| Received on 2007-07-02 Appeared on 2008-04-03 |

**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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