Abstract The nonlinear dynamics and solitonic structures of coupled modified complex Ginzburg–Landau equations with Kerr nonlinearity and Hamiltonian perturbations are examined in this work. Bifurcation analysis is used to find parameter regimes linked to qualitative changes in system behavior once the coupled PDEs have been appropriately transformed into an ordinary differential equation. Poincaré maps, return maps, power spectra, bifurcation diagrams, and Lyapunov exponents with fractal dimensions (box-counting method, correlation sum, and the Kaplan–Yorke dimension) are then used to analyze chaotic dynamics. Furthermore, the generalized exponential rational function method is used to derive accurate traveling-wave solutions of the exponential, trigonometric, and hyperbolic types. The results demonstrate the complexity and uniqueness of the suggested model by highlighting intricate dynamical aspects and exposing multiple families of soliton solutions.
Farooq et al. (2026) studied this question.