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The generalized Boussinesq equations and obliquely interacting solitary waves in a stratified fluid

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Abstract

In this paper, 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. And then by way of them, 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, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120°, the former is slightly weaker than the latter.

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Authors and Affiliations

  1. Institute of Mechanics, Academia Sinica, China

    Dai Shi-qiang

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  1. Dai Shi-qiang
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Shi-qiang, D. The generalized Boussinesq equations and obliquely interacting solitary waves in a stratified fluid. Appl Math Mech 5, 1469–1478 (1984). https://doi.org/10.1007/BF01910437

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  • DOI: https://doi.org/10.1007/BF01910437

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