TY - JOUR
T1 - Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation
AU - Demontis, F.
AU - Lombardo, S.
AU - Sommacal, M.
AU - van der Mee, C.
AU - Vargiu, F.
N1 - Funding Information:
This research has been partially supported by the University of Cagliari and the Regione Autonoma Sardegna in the framework of the “Visiting Professor Call 2015”, which made possible the stay of MS at the Department of Mathematics and Computer Science of the University of Cagliari during the Spring Semester 2015, and by GNFM-INdAM (Gruppo Nazionale per la Fisica Matematica, National Group for Mathematical Physics – Istituto Nazionale di Alta Matematica, National Institute of Advanced Mathematics). MS wishes to express his gratitude for the hospitality of the Department of Mathematics and Computer Science of the University of Cagliari, where part of this article has been written. MS wishes also to thank Northumbria University for allowing him to undertake the said visiting programme abroad.
Publisher Copyright:
© 2018 The Authors
PY - 2018/11
Y1 - 2018/11
N2 - 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.
AB - 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.
KW - Classical Heisenberg ferromagnet equation
KW - Ferromagnetic materials
KW - Inverse scattering transform
KW - Magnetic droplet
KW - Soliton solutions
UR - http://www.scopus.com/inward/record.url?scp=85045741868&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2018.03.020
DO - 10.1016/j.cnsns.2018.03.020
M3 - Article
AN - SCOPUS:85045741868
SN - 1007-5704
VL - 64
SP - 35
EP - 65
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -