Matrix extension of multidimensional dispersionless integrable hierarchies

Autor:	Bogdanov, L. V.
Rok vydání:	2021
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems General Relativity and Quantum Cosmology Mathematical Physics 37K10 37K15 37K25 35Q75
Druh dokumentu:	Working Paper
DOI:	10.1134/S0040577921100019
Popis:	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 $d\geqslant 4$. 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. Comment: 14 pages, to be published in Teor. i Mat. Fiz. (a Russian version)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.14264 Zobrazit plný text záznamu View this record from Arxiv