Modular Schr\"{o}dinger equation and dynamical duality

TL;DR

This paper explores a family of nonlinear Schrödinger equations, revealing dual time evolution scenarios linked by an imaginary time transformation, and develops a unified theoretical framework for these properties.

Contribution

It introduces a unified framework for modular nonlinear Schrödinger equations and uncovers duality in their real-time evolution via analytic continuation.

Findings

Identification of dual time evolution scenarios

Development of a unified theoretical framework

Mapping between real and imaginary time evolutions

Abstract

We discuss quite surprising properties of the one-parameter family of modular (Auberson and Sabatier (1994)) nonlinear Schr\"{o}dinger equations. We develop a unified theoretical framework for this family. Special attention is paid to the emergent \it dual \rm time evolution scenarios which, albeit running in the \it real time \rm parameter of the pertinent nonlinear equation, in each considered case, may be mapped among each other by means of an "imaginary time" transformation (more seriously, an analytic continuation in time procedure).