Integrability of nonlinear wave equations and solvability of their initial value problem

DOI10.1063/1.3699358zbMath1283.37063OpenAlexW2056217485MaRDI QIDQ2860756

Mariano De Leo, D. F. Rial, Antonio Degasperis, Juan Pablo Borgna

Publication date: 20 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3699358

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Initial value problems for nonlinear higher-order PDEs (35G25) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08)

Related Items (4)

Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform ⋮ \(N\)-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium ⋮ Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics ⋮ Rogue waves of wave resonant-interaction equations with the higher-order effects

Cites Work

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• The three-wave resonant interaction equations: Spectral and numerical methods
• Korteweg-de Vries equation: a completely integrable Hamiltonian system
• The Coupled Modified Korteweg-de Vries Equations
• Integrable models in nonlinear optics and soliton solutions
• Integrable nonlocal wave interaction models
• Multicomponent integrable wave equations: I. Darboux-dressing transformation
• New Integrable Equations of Nonlinear Schrodinger Type
• New integrable PDEs of boomeronic type

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