An efficient and highly accurate spectral method for modeling the propagation of solitary magnetic spin waves in thin films

In previous works, it was shown that the propagation of magnetic spin waves in thin films can be approximated by a nonlinear Schrödinger-type equation. The formulation begins with the magnetostatic equations (Gauss and Ampere’s laws of magnetism) and the Landau–Lifshitz equation. The solution of thi...

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Bibliographic Details
Published in:Computational & applied mathematics 2020-09, Vol.39 (3), Article 205
Main Authors: Christou, Marios A., Papanicolaou, Nectarios C., Sophocleous, Christodoulos
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Infinite series
Magnetism
Magnons
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Schrodinger equation
Spectral methods
Thin films
Time dependence
Wave propagation
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Summary:In previous works, it was shown that the propagation of magnetic spin waves in thin films can be approximated by a nonlinear Schrödinger-type equation. The formulation begins with the magnetostatic equations (Gauss and Ampere’s laws of magnetism) and the Landau–Lifshitz equation. The solution of this system is a potential function whose dimensionless amplitude is the solution of a nonlinear Schrödinger. In the current work, we are demonstrating an efficient infinite series solution using the Christov functions. This is the first time the functions are used in problems involving complex arithmetics. The solutions of the time-independent and time-dependent problems are given in complex series form.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01230-7