The generalized Boussinesq equations and obliquely interacting solitary waves in a stratified fluid. (English) Zbl 0579.76117
Summary: On the basis of Boussinesq’s shallow water theory we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. We study the weak interaction of two pairs of obliquely colliding solitary waves, give the second-order approximate solutions for wave profiles and maximum amplitudes, and conclude that when the induced angle between the directions of propagation of impinging solitary waves is less than 120\(\circ\), the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120\(\circ\), the former is slightly weaker than the latter.
Keywords:
Boussinesq’s shallow water theory; generalized Boussinesq equations; weak interaction; obliquely colliding solitary waves; second-order approximate solutionsReferences:
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