Continuous and discrete dynamical Schr\"odinger systems: explicit solutions
Dynamical Systems
2018-03-20 v2 Mathematical Physics
Analysis of PDEs
math.MP
Spectral Theory
Abstract
We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our generalized (GBDT) version of the B\"acklund-Darboux transformation. Asymptotic expansions of these solutions in time are of interest.
Cite
@article{arxiv.1701.08011,
title = {Continuous and discrete dynamical Schr\"odinger systems: explicit solutions},
author = {B. Fritzsche and B. Kirstein and I. Ya. Roitberg and A. L. Sakhnovich},
journal= {arXiv preprint arXiv:1701.08011},
year = {2018}
}
Comments
In this paper, we develop further the approach to the construction of explicit solutions of dynamical systems from arXiv:1603.08709 and arXiv:1609.03451. Some results from arXiv:nlin/0311004 are actively used. In the version 2 of the paper, we consider additionally the asymptotic behaviour of the solutions in time