Darboux transformations for non-Abelian and nonlocal equations of the Toda lattice type

DOI10.1007/BF01016678zbMath0523.35095MaRDI QIDQ584634

M. A. Salle

Publication date: 1982

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

zbMATH Keywords

sine-Gordon equationsdarboux transformationsLangmuir oscillationsnon-Abelian and nonlocal equationsnonlocal Toda equationToda lattice type

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (11)

Non-Abelian Toda lattice and analogs of Painlevé III equation ⋮ Non-abelian evolution systems with conservation laws ⋮ Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations ⋮ Exact solutions of nonlinear Schrödinger equation for positive group velocity dispersion ⋮ Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients ⋮ L-A pairs with rational dependence on spectral parameters. Darboux transformation ⋮ A new two-parameter family of exactly solvable Dirac Hamiltonians ⋮ Asymptotics for the multiple pole solutions of the nonlinear Schrödinger equation ⋮ A binary Darboux transformation for the Toda lattice ⋮ Darboux transformation of the second-type derivative nonlinear Schrödinger equation ⋮ Painlevé type reductions for the non-Abelian Volterra lattices ^*

Cites Work

• Unnamed Item
• Unnamed Item
• Representation of zero curvature for the system of nonlinear partial differential equations \(x_{\alpha,z\bar z}=\exp(kx)_\alpha\) and its integrability
• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• Darboux transformation and the explicit solutions of differential- difference and difference-difference evolution equations. I
• Some comments on the rational solutions of the Zakharov-Schabat equations
• Differential-difference evolution equations. II: Darboux transformation for the Toda lattice
• The decay of the continuous spectrum for solutions of the Korteweg-deVries equation

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