Periodic solutions of Kadomtsev-Petviashvili

DOI10.1016/0001-8708(87)90035-1zbMath0659.35084OpenAlexW2059409175MaRDI QIDQ1112259

Martin jun. Schwarz

Publication date: 1987

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(87)90035-1

zbMATH Keywords

a priori boundsglobal solutionsintegrals of motionuniqueperiodic functionsinitial valueKadomtsev-Petviashvili

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation ⋮ Recent results on the generalized Kadomtsev-Petviashvili equations ⋮ Nonlinear stability of solitary waves of a generalized Kadomtsev-Petviashvili equation ⋮ A uniqueness theorem for the two-dimensional generalized Korteweg de- Vries equation ⋮ Global well-posedness for the KP-I equation on the background of a non-localized solution ⋮ Some generalizations of the Kadomtsev-Petviashvili equations ⋮ Cauchy problem for the generalized Kadomtsev-Petviashvili equation ⋮ Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation ⋮ On the asymptotic behavior of solutions to the (generalized) Kadomtsev-Petviashvili-Burgers equations ⋮ Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction ⋮ On the Cauchy problem for the Kadomtsev-Petviashvili equation ⋮ The Cauchy problem and stability of solitary-wave solutions for RLW--KP-type equations

Cites Work

• Unnamed Item
• Degenerative dispersion laws, motion invariants and kinetic equations
• On a new hierarchy of symmetries for the Kadomtsev-Petviashvili equation
• Recursion operators and bi-Hamiltonian structures in multidimensions. I

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