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Weak and strong interactions between internal solitary waves. (English) Zbl 0548.76020
In this paper the interaction of weakly nonlinear long internal gravity waves has been studied. The authors considered the two-dimensional flow of an inviscid incompressible fluid. Using a Lagrangian formulation the equations of motion were presented in section 2. Weak interactions which occur when the wave phase speeds are unequal were considered in section 3; this case includes that of a head-on collision. It was shown that each wave satisfies a Korteweg-de Vries equation, and the main effect of the interaction is described by a phase shift. Strong interactions occur when the wave phase speeds are nearly equal although the waves belong to different modes. This case was discussed in section 4, and is described by a pair of coupled Korteweg-de Vries equations, for which some interesting numerical results were presented.
Reviewer: L.Y.Shih

MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25Solitary waves (inviscid fluids)