Novel solitary and periodic waves in quadratic-cubic non-centrosymmetric waveguides

TL;DR

This paper explores a broad class of novel solitary and periodic wave solutions in non-centrosymmetric waveguides with quadratic and cubic nonlinearities, including exact algebraic solitary waves, highlighting complex nonlinear wave phenomena.

Contribution

It introduces new analytical solutions for solitary and periodic waves in quadratic-cubic nonlinear waveguides, expanding understanding of wave dynamics in such media.

Findings

Existence of bright, gray, and W-shaped solitary waves.

Derivation of exact algebraic solitary wave solutions.

Identification of conditions for stable wave propagation.

Abstract

We present a wide class of novel solitary and periodic waves in a non-centrosymmetric waveguide exhibiting second- and third-order nonlinearities. We show the existence of bright, gray, and W-shaped solitary waves as well as periodic waves for extended nonlinear Schr\"{o}dinger equation with quadratic and cubic nonlinearities. We also obtained the exact analytical algebraic-type solitary waves of the governing equation, including bright and W-shaped waves. The results illustrate the propagation of potentially rich set of nonlinear structures through the optical waveguiding media. Such privileged waveforms characteristically exist due to a balance among diffraction, quadratic and cubic nonlinearities.