A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions
Abstract
We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algebra of arbitrary rank. This allows us to explicitly derive its particular solutions by using dressing technique. We discuss two classes of solutions over constant background: soliton-like solutions and quasi-rational solutions. Both classes have analogues in the case of the Heisenberg ferromagnet equation for the same Lie algebra and are new even in that special case.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Advanced Mathematical Physics Problems
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Journal of Nonlinear Mathematical Physics
- Volume
- 33
- Issue
- 1
- Publication date
- 12 March 2026
- Language
- EN