The perturbed concatenated model of the Lakshmanan–Porsezian–Daniel and the Sasa–Satsuma equations having the Kerr law in the presence of spatio-temporal dispersion and multiplicative white noise

Abstract

This article examines the traveling wave solutions of the combination of the Lakshmanan–Porsezian–Daniel equation and the Sasa–Satsuma equation with the Kerr law of nonlinearity, perturbation and spatio-temporal dispersion, which have multiplicative white noise. This model is of great significance to communication, optics, physics and other fields. Firstly, the traveling wave transform is substituted into the model for mathematical analysis. Secondly, the dynamical properties and chaotic behaviors of the equation are also analyzed. Finally, by using the trial equation method and the complete discrimination system for polynomial method, more forms of the traveling wave solutions of this equation are obtained. Compared with the previous studies, the new insights in our paper is to find that since the non-average of the solutions still preserves the characteristics of the soliton and periodic modes, otherwise the random average results will destroy these characteristics. The change of amplitude due to the delay factor produced by white noise can be clearly seen through the images.