A Dimensional Integrable Generalization of the Sine‐Gordon Equation I. ‐∂‐Dressing and the Initial Value Problem

DOI10.1002/sapm1993903189zbMath0795.35106OpenAlexW2338343474MaRDI QIDQ4286872

B. G. Konopelchenko, V. G. Dubrovskij

Publication date: 25 September 1994

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1993903189

zbMATH Keywords

dressing methodinverse spectral transformplane breathersplane solitons

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

• Coherent structures for the Ishimori equation. I: Localized solitons with stationary boundaries
• Dromions and a boundary value problem for the Davey-Stewartson 1 equation
• A higher dimension generalization of the Sine-Gordon equation and its soliton theory
• Integrable two-dimensional generalisation of the sine- and sinh-Gordon equations
• On the Solution of the Generalized Wave and Generalized Sine-Gordon Equations
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• The non-local delta problem and (2+1)-dimensional soliton equations
• Backlund transformations via gauge transformations in 2+1 dimensions

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