Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons' propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

College of Humanities and Sciences Ajman University Ajman UAE

Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon

Department of Mathematics Forman Christian College A Chartered University FCCU Lahore Pakistan

Department of Mathematics Namal University Mianwali Pakistan

Department of Mathematics University of the Punjab Lahore Pakistan

IT4Innovations VSB Technical University of Ostrava Poruba Ostrava Czech Republic

PLoS One. 2024 Jul 26;19(7):e0308186. doi: 10.1371/journal.pone.0308186. PubMed

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