On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system

Abstract

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.

15 pages, revised and extended, characterization of the class of reductions in terms of the dressing data is given

References in corpus (2)

• Interpolating Dispersionless Integrable System
• On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

Cited by in corpus (7)

• Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
• `Interpolating' differential reductions of multidimensional integrable hierarchies
• Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
• Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
• Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
• 1+1 spectral problems arising from the Manakov-Santini system
• Dispersionless BKP equation, the Manakov-Santini system and Einstein-Weyl structures