Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations with Self-Consistent Sources: Geometry and Equivalence

Abstract

We propose a new integrable coupled dispersionless equation with self-consistent sources (CDESCS). We obtain the Lax pair and the equivalent generalized Heisenberg ferromagnet equation (GHFE), demonstrating its integrability. Specifically, we explore the geometry of these equations. Last, we consider the relation between the motion of curves/surfaces and the CDESCS and the GHFE.

21 pages

References in corpus (4)

• The short pulse equation is integrable
• On integrability of the vector short pulse equation
• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions

Cited by in corpus (2)

• Dispersionless Limits of Some Integrable Equations
• Dispersionless Limits of Integrable Generalized Heisenberg Ferromagnet Equations