Numerical study of the KP equation for non-periodic waves

@article{Kao2012NumericalSO,
  title={Numerical study of the KP equation for non-periodic waves},
  author={Chiu-Yen Kao and Yuji Kodama},
  journal={Math. Comput. Simul.},
  year={2012},
  volume={82},
  pages={1185-1218}
}
  • C. Kao, Y. Kodama
  • Published 3 April 2010
  • Physics, Computer Science, Mathematics
  • Math. Comput. Simul.
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two-dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and they are called line-soliton solutions in this paper. The classification is based on the far-field patterns of the… Expand
KP solitons in shallow water
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 smallExpand
On a class of initial value problems and solitons for the KP equation: A numerical study
Abstract Recent studies show that the Kadomtsev–Petviashvili (KP) equation admits a large class of exact solutions, referred to as the KP solitons, which are solitary waves localized along distinctExpand
Numerical study of the KP solitons and higher order Miles theory of the Mach reflection in shallow water
In 1970, two Russian physicists Kadomtsev and Petviashvili proposed a twodimensional nonlinear dispersive wave equation to study the stability of the solitary wave solution under the influence ofExpand
Numerical studies of the KP line-solitons
TLDR
The goal is to determine to which of the many exact solutions of the KP equation the initial conditions converge, and the interactions of the evolved solitary wave patterns are studied. Expand
Line‐soliton solutions of the KP equation
A review of recent developments in the study and classification of the line‐soliton solutions of the Kadomtsev‐Petviashvili (KP) equation is provided. Such solution u(x, y, t) is defined by a pointExpand
Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation
The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev–Petviashvili II (KPII) equation. Building upon previous studies that examined theExpand
Two-dimensional interactions of solitons in a two-layer fluid of finite depth
Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle between theExpand
Modulation theory for soliton resonance and Mach reflection
Resonant Y-shaped soliton solutions to the Kadomtsev-Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensionalExpand
Laboratory realization of KP-solitons
Kodama and his colleagues presented a classification theorem for exact soliton solutions of the quasi-two-dimensional Kadomtsev-Petviashvili (KP) equation. The classification theorem is related toExpand
Numerical Analysis of Nonlinear Wave Propagation
Numerical analysis of nonlinear wave propagation Nonlinear partial differential equations (PDEs) arise in many areas of mathematical physics in order to model various physical phenomena. However, inExpand
...
1
2
3
...

References

SHOWING 1-10 OF 27 REFERENCES
FAST TRACK COMMUNICATION: Soliton solutions of the KP equation with V-shape initial waves
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. NumericalExpand
Solitons and the Inverse Scattering Transform
Abstract : Under appropriate conditions, ocean waves may be modeled by certain nonlinear evolution equations that admit soliton solutions and can be solved exactly by the inverse scattering transformExpand
Soliton solutions of the KP equation and application to shallow water waves
The main purpose of this paper is to give a survey of recent development on a classification of soliton solutions of the KP equation. The paper is self-contained, and we give a complete proof for theExpand
Classification of the line-soliton solutions of KPII
In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169–90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of theExpand
Young diagrams and N-soliton solutions of the KP equation
We consider N-soliton solutions of the KP equation, An N-soliton solution is a solution u(x, y, t) which has the same set of N line soliton solutions in both asymptotics y → ∞ and y → −∞. TheExpand
Formation of the rogue wave due to non-linear two-dimensional waves interaction
Abstract It is shown that generation of the rogue waves in the ocean may be described in framework of non-linear two-dimensional shallow water theory where the simplest two-dimensional long waveExpand
Mach reflection and KP solitons in shallow water
Abstract. Reflection of an obliquely incident solitary wave onto a vertical wall is studied analytically and experimentally. We use the Kadomtsev-Petviashivili (KP) equation to analyze the evolutionExpand
Numerical Study of Oscillatory Regimes in the Kadomtsev–Petviashvili Equation
TLDR
The aim of this paper is the accurate numerical study of the Kadomtsev–Petviashvili (KP) equation, and investigates numerically the small dispersion limit of the KP model in the case of large amplitudes. Expand
Solitons and the Inverse Scattering Transform
Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typicalExpand
Solitary water wave interactions
This article concerns the pairwise nonlinear interaction of solitary waves in the free surface of a body of water lying over a horizontal bottom. Unlike solitary waves in many completely integrableExpand
...
1
2
3
...