Relaxing solitons of a biaxial ferromagnet. (English. Russian original) Zbl 1489.82094
Theor. Math. Phys. 210, No. 1, 46-67 (2022); translation from Teor. Mat. Fiz. 210, No. 1, 54-79 (2022).
Summary: We use the Riemann problem on a torus to obtain and analyze new analytic solutions of the Landau-Lifshitz model that describe the nonlinear dynamics of solitons of a biaxial ferromagnet in the field of dispersive spin waves. We show that nonlinear interference of solitons and waves leads to nonadiabatic relaxation oscillations of solitons. Formulas are obtained that determine the changes in the frequency and velocity of solitons in the radiation field. Collisions of relaxing solitons on a spin-wave background are analyzed.
MSC:
| 82D40 | Statistical mechanics of magnetic materials |
| 35C08 | Soliton solutions |
| 35C07 | Traveling wave solutions |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q82 | PDEs in connection with statistical mechanics |
Software:
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