A Generic Nonlinear Evolution Equation of Magnetic Type I. Reductions
Tihomir Valchev
TL;DR
This paper introduces a new integrable nonlinear evolution equation generalizing the Heisenberg ferromagnet model, with specific reductions and a Lax pair structure, contributing to the theory of integrable systems.
Contribution
It presents a novel integrable nonlinear evolution equation of magnetic type, extending classical models with a new Lax pair formulation and reductions.
Findings
The equation is completely integrable.
It admits a linear bundle Lax pair in pole gauge.
Several reductions of the matrix equation are analyzed.
Abstract
The present preprint is dedicated to a nonlinear evolution equation that generalizes the classical Heisenberg ferromagnet equation in certain way. That generalization is completely integrable and has a linear bundle Lax pair in pole gauge related to the special linear algebra. A few reductions of the generic matrix equation are considered.
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Taxonomy
TopicsMatrix Theory and Algorithms · Numerical methods for differential equations · Nonlinear Waves and Solitons