Continuous and discrete dynamical Schrödinger systems: explicit solutions

Abstract

We consider continuous and discrete Schrödinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schrödinger systems). Transformed and explicit solutions are constructed using our generalized (GBDT) version of the Bäcklund-Darboux transformation. Asymptotic expansions of these solutions in time are of interest.

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

References in corpus (4)

• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Inverse problem for one-dimensional dynamical Dirac system (BC-method)
• Dynamical canonical systems and their explicit solutions
• Dynamics of electrons and explicit solutions of Dirac-Weyl systems

Cited by in corpus (1)

• Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches