Inverse scattering for the heat operator and evolutions in \(2+1\) variables (Q1096091)
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scientific article; zbMATH DE number 4030099
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse scattering for the heat operator and evolutions in \(2+1\) variables |
scientific article; zbMATH DE number 4030099 |
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Inverse scattering for the heat operator and evolutions in \(2+1\) variables (English)
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1987
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The asymptotic behavior of functions in the kernel of the perturbed heat operator \(\partial^ 2_ 1-\partial_ 2-u(x)\) suffice to determine u(x). An explicit formula is derived using the \({\bar \partial}\)-method of inverse scattering, complete with estimates for small and moderately regular potentials u. If u evolves so as to satisfy the Kadomtsev- Petviashvili (KP II) equation, the asymptotic data evolve linearly and boundedly. Thus the KP II equation has solutions bounded for all time. A method for calculating nonlinear evolutions related to KP II is presented. The related evolutions include the so-called ``KP II hierarchy'' and many others.
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asymptotic behavior
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perturbed heat operator
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\({\bar \partial }\)-method
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inverse scattering
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Kadomtsev-Petviashvili
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nonlinear evolutions
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