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arXiv · 2105.14264

Matrix extension of multidimensional dispersionless integrable hierarchies

L. V. Bogdanov
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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 $d\geqslant 4$. 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.

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L. V. Bogdanov. 2021-05-29. Matrix extension of multidimensional dispersionless integrable hierarchies. https://doi.org/10.1134/s0040577921100019

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