Exact wave patterns and chaotic dynamical behaviours of the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise

This article examines the exact wave patterns and chaotic dynamical behaviours of the dispersive concatenation model with spatio-temporal dispersion, Hamiltonian perturbation terms and multiplicative white noise. The higher-order dispersion terms of this model have important applications in nonlinear fibre optics. First, an integrating factor equation of the higher-order nonlinear amplitude equation is given by using the trial equation method. Then, combined with bifurcation theory and the complete discrimination system for polynomial method, the topological structure of the dynamical system is analysed, proving the existence of soliton solutions and periodic solutions, and obtaining a series of rich exact solutions, including new solutions. Finally, it is found that the system exhibits chaotic behaviours under appropriate perturbations. In particular, the numerical simulation results show that the non-averaged solutions still preserve the characteristics of solitons and periodic modes. To our knowledge, these results are new for this model and can provide new insights into the study of optical transmission under random perturbations.