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

F. Demontis, Sara Lombardo, Matteo Sommacal, C. Van Der Mee, F. Vargiu

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9 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)35-65
Number of pages31
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume64
Early online date5 Apr 2018
DOIs
Publication statusPublished - 1 Nov 2018

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