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

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Abstract

The asymptotic behavior of functions in the kernel of the perturbed heat operator δ 21 −δ2−u(x) suffice to determineu(x). An explicit formula is derived using the\(\bar \partial \) method of inverse scattering, complete with estimates for small and moderately regular potentialsu. Ifu 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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  1. Department of Mathematics, The University of Georgia, 30602, Athens, Georgia, USA

    Mladen Victor Wickerhauser

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  1. Mladen Victor Wickerhauser
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Communicated by C. H. Taubes

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Wickerhauser, M.V. Inverse scattering for the heat operator and evolutions in 2+1 variables. Commun.Math. Phys. 108, 67–89 (1987). https://doi.org/10.1007/BF01210703

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  • DOI: https://doi.org/10.1007/BF01210703

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