This article is cited in 4 papers

Some thoughts on a nonlinear Schrödinger equation motivated by information theory

R. R. Parwani

National University of Singapore

Abstract: The arguments leading to a nonlinear generalization of the Schrödinger equation in the context of the maximum uncertainty principle are reviewed. The exact and perturbative properties of that equation depend on a free regulating/interpolating parameter $\eta$, which can be fixed using energetics as is shown here. A linear theory with an external potential that reproduces some unusual exact solutions of the nonlinear equation is also discussed, together with possible symmetry enhancements in the nonlinear theory.

Keywords: nonlinear Schrödinger equation, information theory, degeneration.

DOI: 10.4213/tmf6077

 English version: Theoretical and Mathematical Physics, 2007, 152:1, 1012–1016

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