40 citations · 344 across the 59 of their papers we have counts for
63 papers
Dirac systems with locally square-integrable potentials: direct and inverse problems for the spectral functions
Alexander Sakhnovich
We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable…
Hamiltonian systems with several space variables: dressing, explicit solutions and energy relations
Alexander Sakhnovich
We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial ψ}{\partial t}=\sum_{k=1}^r H_k(t)\fr…
Explicit solutions of Schrödinger and KdV equations in terms of square roots of the generalised matrix eigenvalues
Alexander Sakhnovich
In this paper, we consider matrix Schrödinger equation, dynamical Schrödinger equation and matrix KdV. We construct their explicit solutions using our GBDT version of Bäcklund--Dar…
Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications
Alexander Sakhnovich
We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral p…
On essential self-adjointness of singular Sturm-Liouville operators
S. Blake Allan, Fritz Gesztesy, Alexander Sakhnovich
Considering singular Sturm--Liouville differential expressions of the type \[ τ_α = -(d/dx)x^α(d/dx) + q(x), \quad x \in (0,b), \; α\in \mathbb{R}, \] we employ some Sturm comparis…
On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations
Alexander Sakhnovich
We consider canonical systems (with Hamiltonians ), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchm…