Coupled Helmholtz Equations : Chirped Solitary Waves

TL;DR

This paper explores the existence, stability, and chirp reversal phenomena of coupled cubic nonlinear Helmholtz solitary waves, highlighting the effects of non-Kerr nonlinearities and nonparaxial parameters on wave properties.

Contribution

It introduces the analysis of chirp reversal in coupled Helmholtz equations with non-Kerr nonlinearities and studies how nonparaxial parameters influence solitary wave characteristics.

Findings

Chirp reversal occurs under specific nonlinear parameter combinations.

Nonparaxial parameter tuning can control wave speed.

Stable nonparaxial solitary waves are achievable with proper parameters.

Abstract

We investigate the existence and stability properties of the chirped gray and anti-dark solitary waves within the framework of coupled cubic nonlinear Helmholtz equation in the presence of self steepening and self frequency shift. We show that for a particular combination of the self steepening and the self frequency shift, there is not only chirping but also chirp reversal. Specifically, the associated nontrivial phase has two intensity dependent terms, one varies as the reciprocal of the intensity while the other, which depends on non-Kerr nonlinearities, is directly proportional to the intensity. This causes chirp reversal across the solitary wave profile. A different combination of non-Kerr terms leads to chirping but no chirp reversal.The influence of nonparaxial parameter on physical quantities such as intensity, speed and pulse-width of the solitary waves is studied too. It is found that the speed of the solitary waves can be tuned by altering the nonparaxial parameter. Stable propagation of these nonparaxial solitary waves is achieved by an appropriate choice of parameters.