On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equation

TL;DR

This paper derives a broad class of rogue wave solutions for the nonlocal parity-time-symmetric nonlinear Schrödinger equation using a generalized bilinear reduction method, revealing new wave families and unifying previous solutions.

Contribution

It introduces a generalized reduction method to construct extensive rogue wave solutions, including new families, for the PT-symmetric nonlinear Schrödinger equation.

Findings

Derived rogue wave solutions as Gram determinants with Schur polynomial elements.

Included previously known rogue waves as special cases.

Proposed that all rogue waves in this context are encompassed by these solutions.

Abstract

This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue waves are derived as Gram determinants with Schur polynomial elements. It is shown that these rogue waves contain previously reported ones as special cases. More importantly, they contain many new rogue wave families. It is conjectured that the rogue waves derived in this article are all rogue-wave solutions in the parity-time-symmetric nonlinear Schrodinger equation.