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: | Zhou Ruguang, Kui Ying |
Keywords: | geometric modelling, integration |
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.