Time-dependent Schroedinger equation in dimension $k+1$: explicit and rational solutions via GBDT and multinodes

Abstract

A version of the binary Darboux transformation is constructed for non-stationary Schroedinger equation in dimension $k+1$, where $k$ is the number of space variables, $k\ge 1$. This is an iterated GBDT version. New families of non-singular and rational potentials and solutions are obtained. Some results are new for the case that $k=1$ too. A certain generalization of a colligation introduced by M.S. Livsic and of the $S$-node introduced by L.A. Sakhnovich is successfully used in our construction.

References in corpus (4)

• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Solitons and Almost-Intertwining Matrices
• Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
• Harmonic maps, Backlund-Darboux transformations and "line soliton" analogs

Cited by in corpus (3)

• Coordinated Cyber-Attack Detection Model of Cyber-Physical Power System Based on the Operating State Data Link
• Dynamics of electrons and explicit solutions of Dirac-Weyl systems
• Continuous and discrete dynamical Schrödinger systems: explicit solutions