From solitons to chaos: Nonlinear dynamics of the time-fractional modified regularized long-wave equation

Authors

• Samsun Nahar Ananna
• Chunhui Lu
• Abdulla Al Mamun
• Md Al Amin Meia, The University of Texas Rio Grande Valley
• Nur Hasan Mahmud Shahen

Document Type

Article

Publication Date

12-2026

Abstract

This study investigates the nonlinear wave structures and complex dynamical behavior of the time-fractional modified regularized long-wave (mRLW) equation through an integrated analytical, numerical, and dynamical framework, with particular emphasis on connecting localized wave formation with perturbation-induced nonlinear dynamics. Within the adopted fractional framework, a Hirota-type bilinear approach is employed to construct one-wave, two-wave, three-wave, lump, one-lump–one-soliton, and one-lump–one-stripe structures, whose numerical consistency is subsequently examined using the Modified Variational Iteration (MVI) method through graphical comparisons and L 2 and L ∞ error norms. The periodically perturbed mRLW system is further investigated using phase portraits, Lyapunov exponents, bifurcation diagrams, Poincaré sections, return maps, and fractal basin analysis, revealing parameter-dependent transitions from regular wave dynamics to complex and chaotic responses, with a box-counting fractal dimension of D = 1.42120 ± 0.03376 ( R 2 = 0.99383 ) for the investigated basin structure. These findings demonstrate the usefulness of combining analytical wave construction, numerical verification, and nonlinear dynamical diagnostics for characterizing localized structures and complex behavior in fractional nonlinear evolution models.

Comments

© 2026 The Authors. Published by Elsevier B.V. http://creativecommons.org/licenses/by-nc-nd/4.0/

Recommended Citation

Ananna, Samsun Nahar, Chunhui Lu, Abdulla Al Mamun, Md Al Amin Meia, and Nur Hasan Mahmud Shahen. "From Solitons to Chaos: Nonlinear Dynamics of the Time-Fractional Modified Regularized Long-Wave Equation." Physics Open (2026): 100480. https://doi.org/10.1016/j.physo.2026.100480

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Physics Open

DOI

10.1016/j.physo.2026.100480