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

doi:10.1007/s11587-018-0394-8

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 language	English
Pages (from-to)	145-161
Journal	Ricerche di Matematica
Volume	68
Issue number	1
Early online date	4 Apr 2018
DOIs	https://doi.org/10.1007/s11587-018-0394-8
Publication status	Published - 1 Jun 2019

Keywords

Classical Heisenberg ferromagnet equation
Soliton solutions
Inverse scattering transform
Magnetic droplet
Ferromagnetic materials

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10.1007/s11587-018-0394-8

Demontis et al - The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions pt 1 AAMAccepted author manuscript, 184 KB

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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.",

keywords = "Classical Heisenberg ferromagnet equation, Soliton solutions, Inverse scattering transform, Magnetic droplet, Ferromagnetic materials",

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AU - Ortenzi, Giovanni

AU - Sommacal, M.

AU - van der Mee, Cornelis

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

KW - Classical Heisenberg ferromagnet equation

KW - Soliton solutions

KW - Inverse scattering transform

KW - Magnetic droplet

KW - Ferromagnetic materials

UR - https://www.scopus.com/pages/publications/85044973378

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JO - Ricerche di Matematica

JF - Ricerche di Matematica

IS - 1

ER -

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

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