On a class of multidimensional integrable hierarchies and their reductions

Abstract

A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected with Manakov-Santini equation and Dunajski system are considered as illustrative examples.

Talk at NLP5 conference, Gallipoli. 8 pages. Formulae for the second flows of Dunajski equation hierarchy corrected (page 6)

References in corpus (5)

• The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation
• Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
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Cited by in corpus (15)

• `Interpolating' differential reductions of multidimensional integrable hierarchies
• Linearly degenerate hierarchies of quasiclassical SDYM type
• Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
• Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems
• On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system
• Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
• Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
• SDYM equations on the self-dual background
• Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background
• Projective differential geometry of multidimensional dispersionless integrable hierarchies
• Six-dimensional heavenly equation. Dressing scheme and the hierarchy
• Hodograph solutions for the generalized dKP equation
• Integrability properties of symmetric 4+4-dimensional heavenly type equation
• On linear degeneracy of integrable quasilinear systems in higher dimensions
• Matrix extension of multidimensional dispersionless integrable hierarchies