PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators

TL;DR

This paper investigates a generalized PT-symmetric dimer of coupled nonlinear oscillators, analyzing stationary solutions, stability, and dynamics through analytical and numerical methods, including the rotating wave approximation and direct simulations.

Contribution

It introduces a comprehensive analysis of a generalized PT-symmetric nonlinear oscillator dimer, combining analytical and numerical approaches to explore stability and dynamics.

Findings

Identification of stationary solutions and their stability.

Extension of analysis to original oscillator models.

Observation of dynamics through numerical simulations.

Abstract

In the present work, we explore the case of a general PT-symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schr\"odinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.