Tag A. Khare

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

Sep 26, ’14 8:40 PM

J. Cuevas-Maraver, A. Khare, P.G. Kevrekidis, H. Xu, A. Saxena

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 Schrodinger 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.

http://arxiv.org/abs/1409.7218
Pattern Formation and Solitons (nlin.PS); Chaotic Dynamics (nlin.CD); Exactly Solvable and Integrable Systems (nlin.SI)

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PT-Symmetric Dimer of Coupled Nonlinear Oscillators

Jul 24, ’13 11:26 PM

J. Cuevas, P.G. Kevrekidis, A. Saxena, A. Khare

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and anti-symmetric breather solutions, as well as symmetry breaking variants thereof. We propose a reduction of the system to a Schr\”odinger type PT-symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.

http://arxiv.org/abs/1307.6047

Pattern Formation and Solitons (nlin.PS)

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