Breaking of the Butterfly-Four-Wing symmetry in a (3＋1)-dimensional stochastic cylindrical Sasa-Satsuma System: Sensitivity, modulation stability and adjoint of SSS

Hamdy I. Abdel-Gawad and D.M. El-Sakout

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: This study investigates the (3＋1)-dimensional cylindrical Sasa-Satsuma system (Cy-SSS), a key model for ultrashort pulse propagation in optical fibers. It is indeed that an optical fiber is a cylindrical form. So the present study is more realistic to fit with application in Engineering and science. This study is completely novel. The Cy-SSS, is “self-inhomogeneous “as the radios ρ appears explicitly. To study this model equation, a powerful method is needed. So, in the literature, it was only studied via numerical methods or by employing Physics-Informed Neural Networks (PINNs). Here, and for the first time exact analytical solutions for system using the extended unified method, moving beyond common numerical approaches.

Keywords: (3＋1)-dimensional Cy-SSS-spiral vortex; Butterfly with four wings; Symmetry breaking; Stochastic perturbation; The extended unified method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926005710

DOI: 10.1016/j.chaos.2026.118430

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