Solitary wave solution to the nonlinear evolution equation in cascaded quadratic media beyond the slowly varying envelope approximations

TL;DR

This paper derives exact bright and dark soliton solutions for a nonlinear evolution equation in cascaded quadratic media, extending beyond the slowly varying envelope approximation, and discusses the model's integrability.

Contribution

It presents the first exact soliton solutions to the equation beyond the slowly varying envelope approximation, including conditions for their existence.

Findings

Exact bright and dark soliton solutions obtained.

Constraint conditions for soliton existence derived.

Analysis of the model's integrability provided.

Abstract

We report exact bright and dark soliton solution to the nonlinear evolution equation derived by Moses and Wise [Phys. Rev. Lett. 97, 073903, (2006)] for cascaded quadratic media beyond the slowly varying envelope approximations. The integrability aspects of the model are addressed. The traveling wave hypothesis as well as the ansatz method is employed to obtain an exact 1-soliton solution. Both bright and dark soliton solutions are obtained. The corresponding constraint conditions are obtained in order for the soliton solutions to exist.