Coupled Helmholtz equations: Chirped solitary waves

We investigate the existence and stability properties of chirped gray and anti-dark solitary waves within the framework of a coupled cubic nonlinear Helmholtz equation in the presence of self-steepening and a self-frequency shift. We show that for a particular combination of self-steepening and a 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 a nonparaxial parameter on physical quantities, such as intensity, speed, and pulse width of the solitary waves, is studied as well. 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.

Automated summary

In this study, the existence and stability properties of chirped gray and anti-dark solitary waves in a coupled cubic nonlinear Helmholtz equation with self-steepening and a self-frequency shift were investigated. It was found that different combinations of self-steepening and self-frequency shift parameters can lead to chirping and chirp reversal. Additionally, the influence of a nonparaxial parameter on physical quantities of the solitary waves such as intensity, speed, and pulse width was examined, with the discovery that the speed of the solitary waves can be tuned by altering the nonparaxial parameter.