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Register a new userOn a class of multidimensional integrable hierarchies and their reductions
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L.V. Bogdanov
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A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected with Manakov-Santini equation and Dunajski system are considered as illustrative examples.
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We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painleve equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V. 44} (2011), Art. No. 235202.
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