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Download fileEffective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation
journal contribution
posted on 2018-11-08, 11:52 authored by Francesco Demontis, Sara Lombardo, Matteo Sommacal, C. Van Der Mee, Francesca VargiuThe 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
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