On a class of reductions of the Manakov-Santini hierarchy connected with the interpolating system
Abstract
Using the Lax-Sato formulation of the Manakov-Santini hierarchy, we introduce a class of reductions such that the zero-order reduction of this class corresponds to the dKP hierarchy, and the first-order reduction gives the hierarchy associated with the interpolating system introduced by Dunajski. We present the Lax-Sato form of a reduced hierarchy for the interpolating system and also for the reduction of arbitrary order. Similar to the dKP hierarchy, the Lax-Sato equations for L (the Lax function) split from the Lax-Sato equations for M (the Orlov function) due to the reduction, and the reduced hierarchy for an arbitrary order of reduction is defined by Lax-Sato equations for L only. A characterization of the class of reductions in terms of the dressing data is given. We also consider a waterbag reduction of the interpolating system hierarchy, which defines (1+1)-dimensional systems of hydrodynamic type.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- March 2010
- DOI:
- 10.1088/1751-8113/43/11/115206
- arXiv:
- arXiv:0910.4004
- Bibcode:
- 2010JPhA...43k5206B
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 15 pages, revised and extended, characterization of the class of reductions in terms of the dressing data is given