KP solitons in shallow water

@article{Kodama2010KPSI,
  title={KP solitons in shallow water},
  author={Yuji Kodama},
  journal={Journal of Physics A},
  year={2010},
  volume={43},
  pages={434004}
}
  • Y. Kodama
  • Published 26 April 2010
  • Physics, Mathematics
  • Journal of Physics A
The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev–Petviashvili (KP) equation. The KP equation describes weakly dispersive and small amplitude wave propagation in a quasi-two-dimensional framework. Recently, a large variety of exact soliton solutions of the KP equation has been found and classified. These solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and are called… 
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Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution uA(x, y, t) to the KP equation. The contour plot of such a solution provides a tropical
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Special types of exact twoand three-soliton solutions in terms of hyperbolic cosines to the Kadomtsev–Petviashvili II equation are presented, exhibiting rich intriguing interaction patterns on a
On existence of a parameter-sensitive region: quasi-line soliton interactions of the Kadomtsev–Petviashvili I equation
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KP solitons and total positivity for the Grassmannian
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is
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Extreme elevations and slopes of interacting solitons in shallow water
Abstract The paper describes a nonlinear phenomenon of interaction of waves that may be a reason for the existence of high-amplitude wave humps on the sea surface. The properties of extreme elevation
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