Generalized solutions of the shallow water equations are obtained. One studies the particular case of a generalized soliton function passing by a variable bottom. We consider a case of discontinuity in bottom depth. We assume that the surface elevation is given by a step soliton which is defined using generalized solutions (Colombeau 1993). Finally, a system of functional equations is obtained where the amplitudes and celerity of wave are the unknown parameters. Numerical results are presented showing that the generalized solution produces good results having physical sense.
A. C. Alvarez. A. Meril. B. Valiño-Alonso. "Step Soliton Generalized Solutions of the Shallow Water Equations." J. Appl. Math. 2012 (SI09) 1 - 24, 2012. https://doi.org/10.1155/2012/910659