arXiv subjects

Andrei N. Leznov

Publications and source records attributed to Andrei N. Leznov.

2 recordsLinked to original sources

arXiv2023

Integrable mappings for noncommuting objects

We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems. Besides the usual setup with one time and two space dimensions, we consider the case when the unknown functions also depend on two Grassman variables.

hep-th↗

arXiv2023

Multi-soliton solutions of the two-dimensional matrix Davey-Stewartson equation

We explicitly obtain the $m$-soliton solutions of the (1+2)-dimensional matrix Davey-Stewartson equation from the known general solution of the matrix Toda chain with fixed ends. We write these solutions in terms of $m+m$ independent solutions of a pair of linear Shrödinger equations with Hermitian potentials.

hep-th↗