Reciprocal transformations for a spectral problem in \(2+1\) dimensions

DOI10.1007/s11232-009-0064-9zbMath1180.35442OpenAlexW1981824913MaRDI QIDQ1034467

Pilar G. Estevez

Publication date: 6 November 2009

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

Full work available at URL: https://doi.org/10.1007/s11232-009-0064-9

zbMATH Keywords

spectral problemDegasperis-Procesi equationreciprocal transformationVakhnenko-Parkes equation

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Soliton equations (35Q51) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (6)

The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method ⋮ Nonlocal symmetries of some nonlinear partial differential equations with third-order Lax pairs ⋮ Approach in theory of nonlinear evolution equations: the Vakhnenko-Parkes equation ⋮ Miura-reciprocal transformations for non-isospectral Camassa-Holm hierarchies in 2 + 1 dimensions ⋮ Some extensions on the soliton solutions for the Novikov equation with cubic nonlinearity ⋮ Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations

Cites Work

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• Symmetry reductions of a \(2+1\) Lax pair
• A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• Reciprocal transformations and flat metrics on Hurwitz spaces
• Solitons in a nonlinear model medium
• On Reciprocal Bäcklund Transformations and the Korteweg-deVries Hierarchy
• Hodograph transformations for a Camassa–Holm hierarchy in 2 + 1 dimensions
• A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions
• Prolongation algebras and Hamiltonian operators for peakon equations
• A wave equation in 2+1: Painleve analysis and solutions
• Auto-hodograph transformations for a hierarchy of nonlinear evolution equations

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