Pure quartic traveling wave solutions: a numerical study

Area of Science:

• Nonlinear Optics
• Mathematical Physics

Background:

• The nonlinear Schrödinger equation (NLSE) is fundamental for modeling wave propagation in various media.
• Investigating higher-order dispersion terms is crucial for understanding complex wave phenomena.

Purpose of the Study:

• To analyze periodic traveling wave solutions of a pure quartic generalized NLSE.
• To investigate the modulational instability of these solutions.
• To explore the impact of high-order dispersion on spectral stability.

Main Methods:

• Numerical computation of a one-parameter family of dn-oidal-like solutions.
• Comparison with conventional NLSE solutions.
• Numerical analysis of the modulational instability problem.
• Confirmation through numerical simulations.

Main Results:

• A one-parameter family of dn-oidal-like solutions was identified.
• Modulational instability was found to occur in specific parameter intervals, interspersed with stability islands.
• Numerical simulations validated the existence of stable, comb-like spectra.

Conclusions:

• High-order dispersion terms in optical waveguides facilitate the observation of regular and stable comb-like spectra.
• The identified stability islands offer potential for controlled wave propagation.
• This study advances the understanding of nonlinear wave dynamics in generalized NLSE models.