Integrable fermionic extensions of the Garnier system and the anharmonic oscillator

Integrable fermionic extensions of the Garnier system and the anharmonic oscillator

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Article ID: iaor20115693
Volume: 217
Issue: 22
Start Page Number: 9261
End Page Number: 9266
Publication Date: Jul 2011
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: geometric modelling, integration
Abstract:

We first derive a fermionic extension of the Garnier system by applying the method of binary nonlinearization of spectral problem to the supersymmetric KdV equation of Kupershmidt and then a fermionic extension of the anharmonic oscillator by a simple reduction. The integrable properties of resulting systems such as Lax representations, corresponding r‐matrices and conversed integrals of motion are established.

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