Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

TL;DR: In this article, the following problems of the analytic theory of differential equations are considered: Hilbert's 21st problem for Fuchsian systems of linear differential equations, the Birkhoff normal form problem for systems of LDEs with irregular singularities, and the classification problem for isomonodromic deformations of Fuchsians.

TL;DR: In this article, it was argued that in the nonlinear context a separatrix plays the role of an eigenfunction and the initial conditions that spawn the separatrix play the role as an Eigenvalue.

TL;DR: In this article, the authors considered the Itzykson-Zuber-Eynard-Mehta two-matrix model and proved that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's.

TL;DR: In this article, all the ZS-AKNS operators, L = i[∂x−g(x)r(x))−∂ x], which admit two linearly independent families of eigenfunctions, satisfying a differential equation in the spectral parameter λ of the form a(λ)∂λV+B(λ),V=Θ(x),V, are characterized.

TL;DR: In this article, a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable is presented.

TL;DR: The problem of multi-dimensional -algebraic operators is studied in this article, where the Hamiltonian formalism in equations of Lax and Novikov types is considered.