Tag J. Cuevas-Maraver

Entries 2 Total

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 sine-Gordon breathers

Jun 12, ’14 8:23 PM

N. Lu, J. Cuevas-Maraver, P.G. Kevrekidis

In this work, we explore a prototypical example of a genuine continuum breather (i.e., not a standing wave) and the conditions under which it can persist in a \(\mathcal{P T}\)-symmetric medium. As our model of interest, we will explore the sine-Gordon equation in the presence of a \(\mathcal{P T}\)- symmetric perturbation. Our main finding is that the breather of the sine-Gordon model will only persist at the interface between gain and loss that \(\mathcal{P T}\)-symmetry imposes but will not be preserved if centered at the lossy or at the gain side. The latter dynamics is found to be interesting in its own right giving rise to kink-antikink pairs on the gain side and complete decay of the breather on the lossy side. Lastly, the stability of the breathers centered at the interface is studied. As may be anticipated on the basis of their “delicate” existence properties such breathers are found to be destabilized through a Hopf bifurcation in the corresponding Floquet analysis.

http://arxiv.org/abs/1406.3082
Pattern Formation and Solitons (nlin.PS)

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