Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation

Demontis, Francesco, Lombardo, Sara, Sommacal, Matteo, van der Mee, Cornelis and Vargiu, F. (2018) Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation. Communications in Nonlinear Science and Numerical Simulation, 64. pp. 35-65. ISSN 1007-5704

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Official URL: https://doi.org/10.1016/j.cnsns.2018.03.020

Abstract

The non-topological, stationary and propagating, soliton solutions of the classical continuous Heisenberg ferromagnet equation are investigated. A general, rigorous formulation of the Inverse Scattering Transform for this equation is presented, under less restrictive conditions than the Schwartz class hypotheses and naturally incorporating the non-topological character of the solutions. Such formulation is based on a new triangular representation for the Jost solutions, which in turn allows an immediate computation of the asymptotic behaviour of the scattering data for large values of the spectral parameter, consistently improving on the existing theory. A new, general, explicit multi-soliton solution formula, amenable to computer algebra, is obtained by means of the matrix triplet method, producing all the soliton solutions (including breather-like and multipoles), and allowing their classification and description.

Item Type: Article
Uncontrolled Keywords: Classical Heisenberg ferromagnet equation; Soliton solutions; Inverse scattering transform; Magnetic droplet; Ferromagnetic materials
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Paul Burns
Date Deposited: 23 Apr 2018 09:14
Last Modified: 23 Apr 2018 10:13
URI: http://nrl.northumbria.ac.uk/id/eprint/34074

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