Soliton Solutions of the KP Equation with V-Shape Initial Waves

TL;DR

This paper investigates the evolution of V-shape initial waves in the KP equation, demonstrating that solutions tend to specific exact solutions and supporting findings with numerical simulations, chord diagram explanations, and a shallow water experiment.

Contribution

It provides a numerical and experimental analysis of V-shape initial waves in the KP equation, linking asymptotic solutions to recent exact solutions and introducing a chord diagram explanation.

Findings

Solutions approach known exact solutions asymptotically.

Numerical simulations confirm the theoretical predictions.

Experimental shallow water wave observations support the theoretical results.

Abstract

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [Chakravarty and Kodama, JPA, 41 (2008) 275209]. We then use a chord diagram to explain the asymptotic result. We also demonstrate a real experiment of shallow water wave which may represent the solution discussed in this Letter.