Matrix extension of multidimensional dispersionless integrable hierarchies
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Publication:6368869
DOI10.1134/S0040577921100019arXiv2105.14264MaRDI QIDQ6368869
Publication date: 29 May 2021
Abstract: We consistently develop a recently proposed scheme of matrix extension of dispersionless integrable systems for the general case of multidimensional hierarchies, concentrating on the case of dimension . We present extended Lax pairs, Lax-Sato equations, matrix equations on the background of vector fields and the dressing scheme. Reductions, construction of solutions and connections to geometry are discussed. We consider separately a case of Abelian extension, for which the Riemann-Hilbert equations of the dressing scheme are explicitly solvable and give an analogue of Penrose formula in the curved space.
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15)
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