Solitary and periodic waves in quadratic-cubic non-centrosymmetric waveguides

Abstract

We present a wide class of 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 the quadratic-cubic nonlinear Schrödinger equation. We also obtained the exact analytical algebraic-type solitary waves of this model, including bright and W-shaped waves. The results illustrate the propagation of potentially rich set of nonlinear structures through the optical system. Such privileged nonlinear waves characteristically exist due to a balance among diffraction, quadratic and cubic nonlinearities. The stability of the solutions is discussed numerically under finite initial perturbations. These results can be used in studying the propagation of shape-preserved and periodic waves in optical waveguides with quadratic-cubic nonlinearities.