General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equation

TL;DR

This paper explores new types of rogue waves in the nonlocal PT-symmetric nonlinear Schrödinger equation, revealing their explicit forms, diverse behaviors, and complex dynamics, which differ significantly from those in the local NLS equation.

Contribution

The study derives three new types of rogue waves with explicit expressions and analyzes their dynamics, expanding understanding of solutions in nonlocal PT-symmetric NLS equations.

Findings

Three types of rogue waves derived with explicit Schur polynomial expressions

Rogue waves exhibit wider variety and complex polynomial degrees

Dynamics include bounded waves and collapsing singularities, with novel pattern formations

Abstract

Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the local NLS equation. For instance, the polynomial degrees of their denominators can be not only $n(n+1)$, but also $n(n-1)+1$ and $n^2$, where $n$ is an arbitrary positive integer. Dynamics of these rogue waves is also examined. It is shown that these rogue waves can be bounded for all space and time, or develop collapsing singularities, depending on their types as well as values of their free parameters. In addition, the solution dynamics exhibits rich patterns, most of which have no counterparts in the local NLS equation.