Analytical approach for pure high, even-order dispersion solitons

TL;DR

This paper presents an analytical variational approach to model pure high, even-order dispersion solitons, demonstrating their stability and potential application in high energy lasers.

Contribution

It introduces an analytical solution for PHEOD solitons using variational methods and compares these with numerical results, highlighting stability and internal modes.

Findings

Analytical solutions approximate well for dispersion orders ≤8.

All PHEOD solitons are stable according to linear stability analysis.

Internal modes of solitons are identified, aiding high energy laser applications.

Abstract

We theoretically solve the nonlinear Schr\"{o}dinger equation describing the propagation of pure high, even order dispersion (PHEODs) solitons by variational approach. The Lagrangian for nonlinear pulse transmission systems with each dispersion order are given and the analytical solutions of PHEOD soltions are obtained and compared with the numerical results. It is shown that the variational results approximate very well for lower orders of dispersion ($\le 8$) and get worst as the order increasing. In addition, using the linear stability analysis, we demonstrate that all PHEOD solitons are stable and obtain the soliton internal modes that accompany soliton transmission. These results are helpful for the application of PHEOD solitons in high energy lasers.