Related papers: ${\cal PT}$-symmetric coupler with $\chi^{(2)}$ no…
The subject of the work are pairs of linearly coupled PT-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled…
We consider the existence and stability of solitons in a $\chi^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a…
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…
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…
${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime…
We study the families of nonlinear modes described by the nonlinear Schr\"odinger equation with the PT-symmetric harmonic potential $x^2-2i\alpha x$. The found nonlinear modes display a number of interesting features. In particular, we have…
We generalize a finite parity-time (${\cal PT}$-) symmetric network of the discrete nonlinear Schr\"odinger type and obtain general results on linear stability of the zero equilibrium, on the nonlinear dynamics of the dimer model, as well…
Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$…
In the present work we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile. We examine different types of…
In the present paper we consider an optical system with a $\chi^{(2)}$-type nonlinearity and unspecified $\mathcal{PT}$-symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms…
We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system…
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear…
A $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer is a two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic…
In this work we analyze PT-symmetric double-well potentials based on a two-mode picture. We reduce the problem into a PT-symmetric dimer and illustrate that the latter has effectively two fundamental bifurcations, a pitchfork…
In this work, we propose a PT-symmetric coupler whose arms are birefringent waveguides as a realistic physical model which leads to a so-called quadrimer i.e., a four complex field setting. We seek stationary solutions of the resulting…
In the present work, we consider a prototypical example of a PT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT-phase transition in an analytical form. We then focus on the…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…
In the present work we propose a nonlinear anti-$\mathcal{PT}$-symmetric dimer, that at the linear level has been experimentally created in the realm of electric circuit resonators. We find four families of solutions, the so-called upper…
We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a…
Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear…