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Inverse scattering transform for the perturbed 1-soliton potential of the nonstationary Schroedinger and heat equations

Monday 12th November 2001 - 15:00 to 16:00
INI Seminar Room 1
The inverse scattering theory for the nonstationary Schroedinger and heat equations is generalised to include a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Appropriate generalisations of the Jost solutions are introduced and their properties are investigated in detail. The singularity structure of these solutions is shown to be essentially more involved than in the standard case of rapidly decaying potential. Corresponding scattering data are introduced and their singularity structure is investigated as well. Formulation of the inverse problem is given as result of this study.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons