`Interpolating' differential reductions of multidimensional integrable hierarchies

Abstract

We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the four-dimensional case, connected with the second heavenly equation and its generalization proposed by Dunajski. We give a characterization of differential reductions in terms of the Lax-Sato equations as well as in the framework of the dressing method based on nonlinear Riemann-Hilbert problem.

Based on the talk at NLPVI, Gallipoli, 15 pages

References in corpus (3)

• Interpolating Dispersionless Integrable System
• On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
• On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system

Cited by in corpus (8)

• On the Einstein-Weyl and conformal self-duality equations
• The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions
• Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
• Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
• Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
• Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background
• Projective differential geometry of multidimensional dispersionless integrable hierarchies
• Matrix extension of multidimensional dispersionless integrable hierarchies