Wave breaking in solutions of the dispersionless Kadomtsev-Petviashvili equation at a finite time

DOI10.1007/s11232-012-0100-zzbMath1352.35148OpenAlexW2084608504MaRDI QIDQ394866

S. V. Manakov, Paolo Maria Santíni

Publication date: 28 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-012-0100-z

zbMATH Keywords

integrable nonlinear dispersionless partial differential equationwave breaking in multiple dimensionsweakly nonlinear quasi-one-dimensional wave

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Blow-up in context of PDEs (35B44) Soliton solutions (35C08)

Related Items (9)

The Cauchy problem for the Pavlov equation ⋮ Spatial structure of shock formation ⋮ Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation ⋮ Joint application of bilinear operator and F-expansion method for (\(2 + 1\))-dimensional Kadomtsev-Petviashvili equation ⋮ Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations ⋮ Numerical study of break-up in solutions to the dispersionless Kadomtsev-Petviashvili equation ⋮ Whitham modulation theory for the Kadomtsev– Petviashvili equation ⋮ Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations ⋮ On critical behaviour in generalized Kadomtsev-Petviashvili equations

Cites Work

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• Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
• Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation
• A hierarchy of integrable partial differential equations in \(2+1\) dimensions associated with one-parameter families of one-dimensional vector fields
• Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
• On the dispersionless Kadomtsev–Petviashvili equation inn+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories

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