Notes on integrable motion of two interacting curves and two-layer generalized Heisenberg ferromagnet equations

Conference paper
Part of the Trends in Mathematics book series (TM)


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.


two-layer spin system two interacting curves gauge equivalence 

Mathematics Subject Classification (2000)

Primary 53C05 Secondary 53C35 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsEurasian National UniversityNur-SultanKazakhstan
  2. 2.Department of PhysicsEurasian National UniversityNur-SultanKazakhstan

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