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

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

2011-04-13

arxiv.org/abs/1104.2554v1

J. Phys. A: Math. Theor. 44 (2011) 475201

Mathematics

Analysis of PDEs

Scientific paper

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, $k \geq 1$. 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.

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