On time evolutions associated with the nonstationary Schr\"{o}dinger equation
Mathematical Physics
2007-05-23 v1 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
The set of integrable symmetries of the nonstationary Schr\"{o}dinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of time evolutions associated with each of these subsets ultimately lead to nonlinear (possibly, operator) equations of the Kadomtsev--Petviashvili I type or its higher analogues, thus demonstrating that the linear problem itself constructively determines the associated nonlinear integrable evolution equations and their hierarchies.
Cite
@article{arxiv.math-ph/9902014,
title = {On time evolutions associated with the nonstationary Schr\"{o}dinger equation},
author = {A. K. Pogrebkov},
journal= {arXiv preprint arXiv:math-ph/9902014},
year = {2007}
}