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

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

2009-04-17

arxiv.org/abs/0904.2620v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages, 7 figures

Scientific paper

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.

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