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We give here a new class of scalar equations for the Water-Waves problem taking into account variable bottom topographies. Many variable depth KdV equations existing in the literature are recovered as particular cases. We also derive a new linear models for these new equations of same accuracy and we validate numerically these results. We study all these equations and we treat the phenomena of breaking wave.

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Samer Israwi, Ph.D degree in Mathematics from University of Bordeaux 1, France. Full professor, Lebanese University. Born in Beirut 05/07/1983. Doctor in applied Mathematics. His research activity is devoted to PDEs, numerical analysis with applications to oceanography theory.

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