Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

Abstract

In this work, we used the space-time fractional coupled Boussinesq (STFCB) model that is essential tools in the study of quantum optics, steady physics, the variational string’s acoustic waves, ion vibrational frequencies, hydro-magnetic waves in cold plasma and many other fields. In order to put such new precise solutions of the aforementioned model, the modified Sardar-sub equation (MSSE) technique has been suggested with inside the sense of conformable derivative and the fractional order partial differential equation that is capable of changing into an ordinary differential equation by using the travelling wave transform. The scoring of solitons and other solutions demonstrates the MSSE technique compatibility for different constant values, which are shown in 3-D, 2-D and contour plots. Additionally, we discussed the examined model chaotic and dynamical tendencies. The theory of plane dynamical system is used to examine the chaotic patterns of the systems. The investigations are novel and unexamined. They can be utilized to explain the physical phenomena which have been simulated to provide details on the brief dynamical characteristics. According to numerical simulations modifying the parameters of frequencies and amplitudes has an impact on the system of dynamical properties. We indicated that the MSSE technique for creating precise solutions offers new and significant mathematical tools in applied mathematics.