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On a growing mode of the Boussinesq equation. (English) Zbl 1098.76521

Summary: From the summary: The nonlinear evolution of linearly unstable solutions in the Boussinesq system is studied by R. Hirota’s method [J. Math. Phys. 14, 810–814 (1973; Zbl 0261.76008)]. The result shows the peculiar property that the unstable solution neither grows unboundedly nor falls into a saturation level, but attains the maximum amplitude at a certain time, and thereafter damps.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)

Citations:

Zbl 0261.76008
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