PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators

Authors

Jesús Cuevas–Maraver, Universidad de SevillaFollow
Avinash Khare, Indian Institute of Science Education and Research
Panayotis G. Kevrekidis, University of Massachusetts AmherstFollow
Haitao Xu, University of Massachusetts Amherst
Avadh Saxena, Los Alamos National Laboratory

Publication Date

2014

Journal or Book Title

International Journal of Theoretical Physics

Abstract

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 Schrödinger 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.

Comments

Arxiv preprint uploaded. DOI 10.1007/s10773-014-2429-6

Pages

3960–3985

Volume

54

Recommended Citation

Cuevas–Maraver, Jesús; Khare, Avinash; Kevrekidis, Panayotis G.; Xu, Haitao; and Saxena, Avadh, "PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators" (2014). International Journal of Theoretical Physics. 1248.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1248