Related papers: Nonlinear Anti-(Parity-Time) symmetric dimer
A mechanism for asymmetric transport based on the interplay between the fundamental symmetries of parity (P) and time (T) with nonlinearity is presented. We experimentally demonstrate and theoretically analyze the phenomenon using a pair of…
We consider the model of a dual-core spatial-domain coupler with chi^(2) and chi^(3) nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi^(3) terms,…
We address the properties of optical solitons that form in media with competing cubic-quintic nonlinearity and parity-time(PT)-symmetric complex-valued external potentials. The model describes the propagation of solitons in nonlinear…
Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic…
We consider a periodic waveguide array whose unit cell consists of a $\mathcal{PT}$-symmetric quadrimer with two competing loss/gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the…
Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the…
We construct the exact solution of a non-Hermitian $\mathscr{PT}$-symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases we refer to as $A$ and $B$ phases. In the $B$…
A three level atom in $\Lambda$ configuration is reduced to an effective two level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system when subjected to a…
The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the…
We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric…
For the one-dimensional nonlinear Schroedinger equation with a complex potential, it is shown that if this potential is not parity-time (PT) symmetric, then no continuous families of solitons can bifurcate out from linear guided modes, even…
We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…
The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and its dynamical stability are considered in detail. The spontaneous symmetry breaking is found and it is…
Within the standard Lagrangian settings (i.e., the difference between kinetic and potential energies), we discuss and report isochronicity, linearizability and exact solubility of some $n$-dimensional nonlinear position-dependent mass (PDM)…
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
In the actively coupled ($\mathcal{AC}$) pair of waveguides, the growth of small perturbations is saturated by the focussing nonlinearity that couples the linearly growing to the linearly damped mode. On the other hand, in the…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gr\"obner bases is used both to find the conditions on $f(u)$ under which symmetries other than the…