Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-10-21
J. Phys. A: Math. Theor. 43 (2010) 115206
Nonlinear Sciences
Exactly Solvable and Integrable Systems
15 pages, revised and extended, characterization of the class of reductions in terms of the dressing data is given
Scientific paper
Using Lax-Sato formulation of Manakov-Santini hierarchy, we introduce a class of reductions, such that zero order reduction of this class corresponds to dKP hierarchy, and the first order reduction gives the hierarchy associated with the interpolating system introduced by Dunajski. We present Lax-Sato form of reduced hierarchy for the interpolating system and also for the reduction of arbitrary order. Similar to dKP hierarchy, Lax-Sato equations for $L$ (Lax fuction) due to the reduction split from Lax-Sato equations for $M$ (Orlov function), and the reduced hierarchy for arbitrary order of reduction is defined by Lax-Sato equations for $L$ only. 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.
No associations
LandOfFree
On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-143657