Integrable equations in (2+1) dimensions associated with symmetric and homogeneous spaces

DOI10.1063/1.527463zbMath0663.58017OpenAlexW2094335476MaRDI QIDQ3812956

Allan P. Fordy, Chris Athorne

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1063/1.527463

zbMATH Keywords

KdV equationN-wave, Davey-Stewartson, Kadomtsev-Petviashvili equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometry of symmetric spaces (53C35) Partial differential equations of mathematical physics and other areas of application (35Q99) Lie algebras and Lie superalgebras (17B99)

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Cites Work

• General structure of nonlinear evolution equations in 1+2 dimensions integrable by the two-dimensional Gelfand-Dickey-Zakharov-Shabat spectral problem and their transformation properties
• Nonlinear Schrödinger equations and simple Lie algebras
• Two-dimensional Schrödinger operator: inverse scattering transform and evolutional equations
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• Derivative nonlinear Schrodinger equations and Hermitian symmetric spaces
• Generalised KdV and MKdV equations associated with symmetric spaces
• The general structure of integrable evolution equations
• On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions