Nonlinear Waves and Coherent Structures in the Quantum Single-Wave Model

TL;DR

This paper derives and analyzes the quantum single-wave model from fundamental equations, exploring its stability, periodic behaviors, quantum chaos features, and stable solitary-wave solutions through analytical and numerical methods.

Contribution

It introduces the quantum analog of the classical single-wave model, providing new insights into its stability, wave patterns, and chaotic behavior.

Findings

Identified periodic in time patterns analytically and numerically.

Detected features of quantum chaos in the unstable parameter region.

Found stable solitary-wave solutions in the quantum single-wave model.

Abstract

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the quantum single-wave model has been studied, and periodic in time patterns have been found both analytically and numerically. In addition, some features of quantum chaos have been detected in the unstable region in parameter space. Further, a class of standing-wave solutions of the quantum single-wave model has also been found, which have been observed to behave as stable solitary-wave structures. The analytical results have been finally compared to the exact system dynamics obtained by solving the corresponding equations in Schrodinger representation numerically.