Numerical study of the KP equation for non-periodic waves

DOI10.1016/j.matcom.2010.05.025zbMath1248.65107arXiv1004.0407OpenAlexW1969784658MaRDI QIDQ446029

Yuji Kodama, Chiu-Yen Kao

Publication date: 28 August 2012

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.0407

zbMATH Keywords

convergencenumerical examplesinitial value problempseudo-spectral methodsoliton solutionsKadomtsev-Petviashvili equationshallow water wave problemchord diagramswave propagatingwindow technique

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (13)

Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation ⋮ Stability of line solitons for the KP-II equation in ℝ² ⋮ On a class of initial value problems and solitons for the KP equation: a numerical study ⋮ Evolution of truncated and bent gravity wave solitons: the Mach expansion problem ⋮ Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations ⋮ Numerical studies of the KP line-solitons ⋮ Deformed solitons of a typical set of (2+1)-dimensional complex modified Korteweg-de Vries equations ⋮ Topographic effect on oblique internal wave–wave interactions ⋮ The KP theory and Mach reflection ⋮ Soliton Solutions of the KP Equation and Application to Shallow Water Waves ⋮ Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation ⋮ Integrability, exact reductions and special solutions of the KP–Whitham equations ⋮ On diffraction and oblique interactions of horizontally two-dimensional internal solitary waves

Cites Work

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• Soliton Solutions of the KP Equation and Application to Shallow Water Waves
• The inverse scattering transform: Semi-infinite interval
• Resonantly interacting solitary waves
• Young diagrams and N-soliton solutions of the KP equation
• Solitary water wave interactions

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