Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems

Christian, JM; McDonald, GS; Lundie, MJ; Kotsampaseris, A

Abstract

We consider an envelope equation with space-time symmetry for describing scalar waves in systems with spatiotemporal dispersion and a generic saturable nonlinearity. Exact bright and gray solitons are derived by direct integration methods and coordinate transformations, with the results for cubic-quintic systems [see companion article— Phys. Rev. A 98, 053842 (2018)] recovered in the limit of weak saturation. Classic predictions from a nonlinear Schrödinger formulation of the propagation problem are shown to emerge asymptotically as subsets of the more general spatiotemporal solutions. The robustness of the new solitons against perturbations to the local pulse shape is then tested by deploying integral stability criteria, symmetry principles, and numerical analysis.

Citation

Christian, J., McDonald, G., Lundie, M., & Kotsampaseris, A. (2018). Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems. Physical Review A, 98(5), 053843. https://doi.org/10.1103/PhysRevA.98.053843

• Journal Article Type: Article
• Acceptance Date: Nov 26, 2018
• Online Publication Date: Nov 26, 2018
• Publication Date: Nov 26, 2018
• Deposit Date: Mar 20, 2019
• Publicly Available Date: Mar 20, 2019
• Journal: Physical Review A
• Print ISSN: 1050-2947
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Volume: 98
• Issue: 5
• Pages: 053843
• DOI: https://doi.org/10.1103/PhysRevA.98.053843
• Publisher URL: https://doi.org/10.1103/PhysRevA.98.053843
• Related Public URLs: https://journals.aps.org/pra/