INTEGRABLE SYSTEMS IN SYMPLECTIC GEOMETRY

ASADI, E. ; SANDERS, J. A.

Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 5-23

Résumé

Quaternionic vector mKDV equations are derived from the Cartan structure equation in the symmetric space = Sp(n+1)/Sp(1) × Sp(n). The derivation of the soliton hierarchy utilizes a moving parallel frame and a Cartan connection 1-form ω related to the Cartan geometry on modelled on . The integrability structure is shown to be geometrically encoded by a Poisson–Nijenhuis structure and a symplectic operator.

Détail

DOI : 10.1017/S0017089508004746

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