The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. II. IST and closed-form soliton solutions
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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.
KeywordsClassical Heisenberg ferromagnet equation Soliton solutions Inverse scattering transform Magnetic droplet Ferromagnetic materials
Mathematics Subject Classification35C08 35G25 35P25 35Q40 35Q51
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.
- 5.Demontis, F., Ortenzi, G., Sommacal, M., van der Mee, C.: The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory. Ricerche Mat. (2018). https://doi.org/10.1007/s11587-018-0394-8
- 15.Ivanov, B., Kosevich, A.: Bound-states of a large number of magnons in a ferromagnet with one-ion anisotropy. Zh. Eksp. Teor. Fiz. 72(5), 2000–2015 (1977)Google Scholar
- 25.Demontis, F., Lombardo, S., Sommacal, M., van der Mee, C., Vargiu, F.: Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation (submitted)Google Scholar
- 26.Chen, A.-H., Wang, F.-F.: Darboux transformation and exact solutions of the continuous Heisenberg spin chain equation. Z. Nat. Teil A 69, 9–16 (2014)Google Scholar
- 27.Yersultanova, Z.S., Zhassybayeva, M., Yesmakhanova, K., Nugmanova, G., Myrzakulov, R.: Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials. Int. J. Geom. Methods Mod. Phys. 13, 1550134 (2016)MathSciNetCrossRefMATHGoogle Scholar
- 36.Demontis, F.: Matrix Zakharov–Shabat system and inverse scattering transform (2012), also: Direct and inverse scattering of the matrix Zakharov–Shabat system. Ph.D. Thesis, University of Cagliari, Italy (2007)Google Scholar
- 37.Dym, H.: Linear Algebra in Action, Vol. 78, Graduate Studies in Mathematics. American Mathematical Society, Providence (2007)Google Scholar
- 38.van der Mee, C.: Nonlinear evolution models of integrable type, vol. 11, e-Lectures Notes, SIMAI (2013)Google Scholar
- 42.Schiebold, C.: Asymptotics for the multiple pole solutions of the nonlinear Schrödinger equation. Mid Sweden University, Reports of the Department of Mathematics 1, 51 pages (2014)Google Scholar