Inverse Spectral Transform for the Nonlinear Evolution Equation Generating the Davey-Stewartson and Ishimori Equations

DOI10.1002/sapm1990824319zbMath0705.35133OpenAlexW2500736170MaRDI QIDQ3485354

B. G. Konopelchenko, B. T. Matkarimov

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1002/sapm1990824319

zbMATH Keywords

initial-value problemDavey-StewartsonIshimori equationschiral-fieldinverse-spectral-transform

Mathematics Subject Classification ID

Riemann-Hilbert problems in context of PDEs (35Q15) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items (11)

\( \overline{\partial} \)-dressing method for the nonlocal mKdV equation ⋮ Remarks on matrix hierarchies, d bar dressing, and the spectral transform ⋮ Application of the \(\bar\partial \)-dressing method to a \((2+1)\)-dimensional equation ⋮ A \(2+1\) dimensional Volterra type system with nonzero boundary conditions via Dbar dressing method ⋮ Relations between hierarchies and inverse scattering ⋮ \(\bar{\partial}\)-dressing method for the \((2+1)\)-dimensional Korteweg-de Vries equation ⋮ Dbar-dressing method for the Gerdjikov-Ivanov equation with nonzero boundary conditions ⋮ The Cauchy problem for the Ishimori equations ⋮ \( \overline{\partial} \)-dressing method for the coupled Gerdjikov-Ivanov equation ⋮ IST Versus PDE: A Comparative Study ⋮ A \(\overline{\partial}\)-dressing approach to the Kundu-Eckhaus equation

Cites Work

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• On a spectral transform of a KDV-like equation related to the Schrodinger operator in the plane
• The non-local delta problem and (2+1)-dimensional soliton equations
• Two-dimensional lumps in nonlinear dispersive systems
• Linear spectral problems, non-linear equations and the δ-method
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

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