A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Nearly one century after the birth of quantum mechanics, parity–time symmetry is
revolutionizing and extending quantum theories to include a unique family of non-Hermitian …

The first good prediction of the multipole soliton solution for the non-integrable equation, ie,
the saturable nonlinear Schrödinger equation under the PT-symmetric potential, is achieved …

Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

We present a survey of some recent theoretical and experimental studies on nonlinear
waves that form and propagate in a broad class of optical and matterwave media. The article …

Both theoretical and experimental studies of topological phases in non-Hermitian systems
have made a remarkable progress in the last few years of research. In this article, we review …

One of the challenges of the modern photonics is to develop all‐optical devices enabling
increased speed and energy efficiency for transmitting and processing information on an …

Controlling light transport in nonlinear active environments is a topic of considerable interest
in the field of optics. In such complex arrangements, of particular importance is to devise …

Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is
analyzed in both one-and two-dimensional systems. First we show analytically that when the …

We investigate the dynamical behavior of continuous and discrete Schrödinger systems
exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a …