Inverse scattering for the heat operator and evolutions in \(2+1\) variables

DOI10.1007/BF01210703zbMath0633.35070MaRDI QIDQ1096091

Mladen Victor Wickerhauser

Publication date: 1987

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

zbMATH Keywords

asymptotic behaviorinverse scatteringKadomtsev-Petviashvilinonlinear evolutions\({\bar \partial }\)-methodperturbed heat operator

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Cites Work

• Unnamed Item
• Unnamed Item
• 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
• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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