Theoretical Study on Spatial Ring Formation and Stabilization of Spatiotemporal Solitons

V. Sabeer

Department of Physics, Korambayil Ahamed Haji Memorial Unity Women’s College (Autonomous), Manjeri, University of Calicut, 676122, Kerala, India.

N. K. Hashim

Department of Physics, W M O Arts and Science College, Muttil, Kerala, India.

A. K. Shafeeque Ali *

Department of Physics, Sullamussalam Science College (Autonomous), University of Calicut, Areekode, 673639 Kerala, India.

*Author to whom correspondence should be addressed.


Abstract

Spatiotemporal solitons become dynamically unstable in an unbalanced nonlinear medium. This study examines the conditions that enable stable propagation in both negative-index and positive-index regimes of metamaterials (MMs). Using Lagrangian variational analysis and the split-step Fourier method, we show that three-dimensional light bullets remain stable under specific conditions. In the negative-index regime, stability occurs when normal dispersion balances defocusing cubic and focusing quintic nonlinearities. In the positive-index regime, stability arises when anomalous dispersion interacts with focusing cubic and defocusing quintic nonlinearities. We also observe the formation of spatial rings during the propagation of a Gaussian beam in certain regimes of nonlinearity and dispersion. These results provide new insight into soliton dynamics in MMs and may enable applications in optical communications, photonics, and nonlinear optics.

Keywords: Spatiotemporal solitons, light bullets, nonlinear metamaterials, negative-index metamaterials, cubic-quintic nonlinearity, Lagrangian variational analysis, split-step Fourier method, spatial ring formation, optical pulse propagation, soliton stabilisation


How to Cite

Sabeer, V., N. K. Hashim, and A. K. Shafeeque Ali. 2026. “Theoretical Study on Spatial Ring Formation and Stabilization of Spatiotemporal Solitons”. Journal of Advances in Mathematics and Computer Science 41 (8):1-10. https://doi.org/10.9734/jamcs/2026/v41i82183.

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