On the N-wave Equations with PT-symmetry

TL;DR

This paper explores PT-symmetric extensions of N-wave systems, analyzing their integrability, reductions, and soliton solutions, with specific examples demonstrating the existence of regular multi-solitons under certain conditions.

Contribution

It introduces new PT-symmetric reductions of N-wave systems and examines their soliton solutions, expanding understanding of integrable models with nonlocal symmetries.

Findings

PT-symmetric N-wave systems admit nonlocal reductions.

Certain 3-wave equations have regular multi-soliton solutions.

Properties of 1- and 2-soliton solutions are characterized.

Abstract

We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.