Related papers: $\mathcal{PT}$-symmetric ladders with a scattering…
We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multi-core waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear…
We introduce a new unified two-parameter $\{(\epsilon_x, \epsilon_t)\,|\epsilon_{x,t}=\pm1\}$ wave model (simply called ${\mathcal Q}_{\epsilon_x,\epsilon_t}^{(n)}$ model), connecting integrable local and nonlocal vector nonlinear…
$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by…
We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In…
We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schr\"odinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior…
We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer…
We theoretically investigate the solitary waves and their switching dynamics in a $\mathcal{PT}$-symmetric directional fiber coupler, exhibiting Kerr nonlinearity, by developing a variational analysis. We analyze the fundamental switching…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
The subject of PT-symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schr\"odinger model with a complex potential that can be tuned controllably away from being PT-symmetric, as it…
Context: Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics. Aims: We aim to show how PT and anti-PT symmetries determine the…
The effect of derivative nonlinearity and parity-time- (PT-) symmetric potentials on the wave propagation dynamics is investigated in the derivative nonlinear Schrodinger equation, where the physically interesting Scarff-II and…
Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…
We show that a pair of coupled nonlinear oscillators, of which one oscillator has positive and the other one negative damping of equal rate, can form a Hamiltonian system. Small-amplitude oscillations in this system are governed by a…
Ladder polymers, known for their rigid, ladder-like structures, exhibit exceptional thermal stability and mechanical strength, positioning them as candidates for advanced applications. However, accurately determining their structure from…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking…
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…
We investigate experimentally parity-time (${\cal PT}$) symmetric scattering using $LRC$ circuits in an inductively coupled ${\cal PT}$- symmetric pair connected to transmission line leads. In the single-lead case, the ${\cal PT}$-symmetric…