4,770 research outputs found
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
We consider two-component integrable generalizations of the dispersionless
2DTL hierarchy connected with non-Hamiltonian vector fields, similar to the
Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a
one-parametric family connected by hodograph type transformations. Generating
equations and Lax-Sato equations are introduced, a dressing scheme based on the
vector nonlinear Riemann problem is formulated. The simplest two-component
generalization of the dispersionless 2DTL equation is derived, its differential
reduction analogous to the Dunajski interpolating system is presented. A
symmetric two-component generalization of the dispersionless elliptic 2DTL
equation is also constructed.Comment: 10 pages, the text of the talk at NEEDS 09. Notations clarified,
references adde
`Interpolating' differential reductions of multidimensional integrable hierarchies
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.Comment: Based on the talk at NLPVI, Gallipoli, 15 page
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