Oblique Interaction of Solitons in an Extended Kadomtsev–Petviashvili Equation

Abstract

Oblique interaction of two solitons of the same amplitude in an extended Kadomtsev–Petviashvili (EKP) equation, which is a weakly two-dimensional generalization of an extended Korteweg–de Vries (EKdV) equation, is investigated. This interaction problem is solved numerically under the initial and boundary condition simulating the reflection problem of the obliquely incident soliton due to a rigid wall. The essential parameters are given by Q^*≡aQ and Ω^*≡Ω⁄a^1⁄2. Here, Q is the coefficient of the cubic nonlinear term in the EKP quation, a the amplitude of the incident soliton and Ω≡tanθ_i, θ_i being the angle of incidence. The numerical solutions for various values of these parameters reveal the effect of the cubic nonlinear term on the behavior of the waves generated by the interaction. When Q^* is small, the interaction property is very similar to that of the Kadomtsev–Petviashvili equation. Especially, for relatively small Ω^*, a new wave of large amplitude and of soliton profile called “stem” is generated. On the other hand, when Q^* is close to 6, no stem is generated owing to the existence of amplitude restriction for the soliton solution.