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

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posted on 08.11.2018, 11:52 by Francesco Demontis, Sara LombardoSara Lombardo, Matteo Sommacal, C. Van Der Mee, Francesca Vargiu
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

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Nonlinear Science and Numerical Simulation

Volume

64

Pages

35 - 65

Citation

DEMONTIS, 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.

Publisher

© The Authors. Published by Elsevier

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Acceptance date

29/03/2018

Publication date

2018

Notes

This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

ISSN

1007-5704

Language

en