# The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. II. IST and closed-form soliton solutions

• F. Demontis
• G. Ortenzi
• M. Sommacal
• C. van der Mee
Article

## Abstract

A new, general, closed-form soliton solution formula for the classical Heisenberg ferromagnet equation with in-plane asymptotic conditions is obtained by means of the inverse scattering transform technique and the matrix triplet method. This formula encompasses the soliton solutions already known in the literature as well as a new class of soliton solutions (the so-called multipole solutions), allowing their classification and description. Examples from all classes are provided and discussed.

## Keywords

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

## Mathematics Subject Classification

35C08 35G25 35P25 35Q40 35Q51

## 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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© 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