The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions: I. Direct and inverse scattering theory

Francesco Demontis, Giovanni Ortenzi, M. Sommacal, Cornelis van der Mee

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Abstract

We develop the direct and inverse scattering theory of the linear eigenvalue problem associated with the classical Heisenberg continuous equation with in-plane asymptotic conditions. In particular, analyticity of the scattering eigenfunctions and scattering data, and their asymptotic behaviours are derived. The inverse problem is formulated in terms of Marchenko equations, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided.
Original languageEnglish
Pages (from-to)145-161
JournalRicerche di Matematica
Volume68
Issue number1
Early online date4 Apr 2018
DOIs
Publication statusPublished - 1 Jun 2019

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