On the initial value problem for a completely integrable shallow water wave equation. (English) Zbl 1002.76012

Summary: We present an algorithm for solving the initial value problem on the infinite line for a wave equation arising in the study of long waves at the free surface of water. The algorithm exploits a link between the hierarchy of shallow water equations and that of the modified Korteweg-de Vries equations.


76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
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