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INTEGRABLE SYSTEMS IN SYMPLECTIC GEOMETRY

Published online by Cambridge University Press:  01 February 2009

E. ASADI  and
J. A. SANDERS
E. ASADI
Affiliation:
Department of Mathematics, Faculty of Sciences, Vrije Universiteit, Amsterdam, The Netherlands
J. A. SANDERS
Affiliation:
Department of Mathematics, Faculty of Sciences, Vrije Universiteit, Amsterdam, The Netherlands
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009 , pp. 5 - 23
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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