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Paper detail

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

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.

preprint2011arXivOpen access
A. L. Sakhnovich
math.APmath-phmath.FAmath.MP
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A. L. Sakhnovich

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