Dynamical Properties, Exact Solutions, and Chaotic Behaviors of the Concatenation Model With Multiplicative White Noise

In this paper, a concatenation model with nonlinear Kerr's law is studied in detail with the presence of spatio‐temporal dispersion, Hamiltonian disturbance terms, and multiplicative white noise. The trial equation method is applied to give an integral factor equation of high order nonlinear amplitude equation, and bifurcation theory is employed to analyze the Hamiltonian and topological properties to the reduced system. Then, the stochastic single traveling wave solutions to the equation are obtained in terms of soliton solutions, singular solutions, and Jacobian elliptic function periodic solutions by the complete discrimination system for polynomial method. Among those, there exist new solutions. Furthermore, the averaging values of the solutions under Brownian motion are given, and it is found that there is a delay factor so that the white noise affects not only the phase factors but also the amplitudes of the solutions. Additionally, the chaotic behaviors of the model are also discovered by taking the external perturbed terms into consideration.