This chapter introduces the basic ideas of P T-symmetric systems. It begins with a brief
discussion of closed (isolated) and open (non-isolated) systems and explains that P T …

We construct certain higher order smooth positon and breather positon solutions of an
extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity. We utilize …

We construct several new integrable systems corresponding to nonlocal versions of the
Hirota equation, which is a particular example of higher order nonlinear Schrödinger …

We construct the optical smooth positon solutions for the generalized variable coefficient
nonlinear Schrödinger equation with longitudinally varying dispersion, nonlinearity, linear …

The formation of rogue waves in shallow water is presented in this Rapid Communication by
providing the three lowest-order exact rational solutions to the Korteweg–de Vries (KdV) …

We construct two kinds of degenerate soliton solutions, one on the zero background and
another on the plane wave background for the coupled Hirota equation. In the case of zero …

We present an overview of some key results obtained in a recent series devoted to non-
Hermitian quantum field theories for which we systematically modify the underlying …

Following a generic approach that leads to Bogomolny–Prasad–Sommerfield (BPS) soliton
solutions by imposing self-duality, we investigate three different types of non-Hermitian field …

We construct all higher order conserved charges from a general two-dimensional zero
curvature condition using a Gardner transformation. Employing two of those charges in the …

A class of complex breather and soliton solutions to both KdV and mKdV equations are
identified with a Pöschl-Teller type PT-symmetric potential. However, these solutions …