Integrable G-strands on semisimple Lie groups

François Gay-Balmaz (1) , Darryl D Holm (2) , Tudor S Ratiu (3)

1 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)
2 Department of Mathematics [Imperial College London]
3 Département de Mathématiques - EPFL

The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamilton's principles and Hamiltonians for these systems, and analyzes the linear stability of their equilibrium solutions in the examples of and .

Domaines: Physique mathématique [math-ph]

François Gay-Balmaz, Darryl D Holm, Tudor S Ratiu. Integrable G-strands on semisimple Lie groups. Journal of Physics A: Mathematical and Theoretical, 2014, 47 (7), pp.075201. ⟨10.1088/1751-8113/47/7/075201⟩. ⟨hal-01083760⟩