Soliton Solutions of the KP Equation with V-Shape Initial Waves
Exactly Solvable and Integrable Systems
2015-05-13 v1 Mathematical Physics
math.MP
Pattern Formation and Solitons
Fluid Dynamics
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.
Cite
@article{arxiv.0904.2620,
title = {Soliton Solutions of the KP Equation with V-Shape Initial Waves},
author = {Yuji Kodama and Masayuki Oikawa and Hidekazu Tsuji},
journal= {arXiv preprint arXiv:0904.2620},
year = {2015}
}
Comments
4 pages, 7 figures