Geodesic
INTEGRABLE SYSTEMS IN SYMPLECTIC GEOMETRY
Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 5-23

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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. 
ASADI, E.; SANDERS, J. A. INTEGRABLE SYSTEMS IN SYMPLECTIC GEOMETRY. Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 5-23. doi: 10.1017/S0017089508004746
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     title = {INTEGRABLE {SYSTEMS} {IN} {SYMPLECTIC} {GEOMETRY}},
     journal = {Glasgow mathematical journal},
     pages = {5--23},
     year = {2009},
     volume = {51},
     number = {A},
     doi = {10.1017/S0017089508004746},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004746/}
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