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

  • F. Demontis
  • G. Ortenzi
  • M. Sommacal
  • C. 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.

Keywords

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

Mathematics Subject Classification

35C08 35G25 35P25 35Q40 35Q51 
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Notes

Acknowledgements

The results contained in the present paper have been partially presented in Wascom 2017. The research leading to this article was supported in part by INdAM-GNFM and the London Mathematical Society Scheme 4 (Research in Pairs) grant on “Propagating, localised waves in ferromagnetic nanowires” (Ref No: 41622). We also wish to thank an anonymous referee for his/her valuable comments.

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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  • F. Demontis
    • 1
  • G. Ortenzi
    • 2
  • M. Sommacal
    • 3
  • C. van der Mee
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di CagliariCagliariItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano BicoccaMilanItaly
  3. 3.Department of Mathematics, Physics and Electrical EngineeringUniversity of Northumbria at NewcastleNewcastle upon TyneUK

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