The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns

Abstract

The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe stationary moving symmetric wave patterns consisting of two plane solitary waves of equal amplitudes moving at an angle to each other. The results obtained within the approximate asymptotic theory are validated by comparison with the exact two-soliton solution of the Kadomtsev–Petviashvili equation (KP2-equation). The suggested approach is equally applicable to a wide class of non-integrable equations too. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin–Ono equation describing internal waves in the infinitely deep ocean containing a relatively thin one of the layers.

Keywords

• Kadomtsev–Petviashvili equation
• Benjamin–Ono equation
• asymptotic theory
• solitary waves
• two-soliton solution
• phase shift