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Soliton Excitations in Terms of Pseudo‐Riemannian Manifolds
Author(s) -
Wiatrowski G.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221290219
Subject(s) - soliton , isotropy , superposition principle , physics , manifold (fluid mechanics) , metric (unit) , space (punctuation) , motion (physics) , spacetime , anisotropy , classical mechanics , deformation (meteorology) , riemannian geometry , riemannian manifold , mathematical physics , mathematical analysis , quantum mechanics , mathematics , nonlinear system , mechanical engineering , linguistics , operations management , philosophy , meteorology , engineering , economics
Advantages are shown of description of one‐dimensional ferromagnetic soliton excitations in an anisotropic medium in terms of a pseudo‐Riemannian manifold. The soliton appears then as a solution of a linear equation of motion of the Schrödinger type in an isotropic curved space of observations equipped with a pseudo‐Riemannian metric. Physically this describes, in particular, the temporal fluctuations of the system, and the change of the exchange interactions as well as predicts the superposition of solitons. The approach enables a consistent explanation of the decay of soliton and space deformation as well.