Notes on integrable motion of two interacting curves and two-layer generalized Heisenberg ferromagnet equations
- Resource Type
- Authors
- Ratbay Myrzakulov; Zhaidary Myrzakulova; Gulgassyl Nugmanova
- Source
- Trends in Mathematics ISBN: 9783030340711
- Subject
- Physics
Ferromagnetism
Integrable system
Two layer
Motion (geometry)
Condensed Matter::Strongly Correlated Electrons
Differential geometry of curves
Gauge (firearms)
Korteweg–de Vries equation
Equivalence (measure theory)
Mathematical physics
- Language
We study the integrable two-layer generalized Heisenberg ferromagnet equation (HFE). The relation between this generalized HFE and differential geometry of curves is established. Using this relation we found the geometrical equivalent counterpart of the two-layer spin system which is the two-component KdV equation. Finally, the gauge equivalence between these equations is established.