https://journaljamcs.com/index.php/JAMCS <p style="text-align: justify;"><strong>Journal of Advances in Mathematics and Computer Science (ISSN:&nbsp;2456-9968)</strong> aims to publish original research articles, review articles and short communications, in all areas of mathematics and computer science. Subject matters cover pure and applied mathematics, mathematical foundations, statistics and game theory, use of mathematics in natural science, engineering, medicine, and the social sciences, theoretical computer science, algorithms and data structures, computer elements and system architecture, programming languages and compilers, concurrent, parallel and distributed systems,&nbsp; telecommunication and networking, software engineering, computer graphics, scientific computing, database management, computational science, Artificial Intelligence, human-computer interactions, etc. By not excluding papers based on novelty, this journal facilitates the research and wishes to publish papers as long as they are technically correct and scientifically motivated. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open-access INTERNATIONAL journal.</p> <p>&nbsp;</p> SCIENCEDOMAIN international en-US Journal of Advances in Mathematics and Computer Science 2456-9968 https://journaljamcs.com/index.php/JAMCS/article/view/2183 <p>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.</p> V. Sabeer N. K. Hashim A. K. Shafeeque Ali Copyright (c) 2026 Author(s). The licensee is the journal publisher. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2026-07-11 2026-07-11 41 8 1 10 10.9734/jamcs/2026/v41i82183