Bifurcation, Chaotic behavior, Sensitivity Analysis, and Optical Soliton Solutions to the Time-fractional Symmetric Regularised-Long-Wave Equation

Abstract

The time-fractional Symmetric Regularized-Long-Wave equation that emerges in simulations of long-term water flow models is efficiently solved in this paper using a new auxiliary equation method. The model takes into consideration the conformable fractional derivatives. Bell-shaped, anti-bell-shaped, kink, and anti-kink soliton solutions are obtained using this method. To illustrate the spatial and temporal evolution properties of the generated solutions, two-dimensional, contour, and three-dimensional diagrams are drawn. Additionally, a planar dynamical system is obtained using galilean transformation in order to conduct the bifurcation analysis, chaotic behaviour, and sensitivity of the model. The study offers crucial information on the stability of the solutions and the reactions that take place when different types of solutions are used. Whenever a parameter varies, bifurcation analysis is used to examine how the qualitative behaviour of the system changes. Additionally, it offers better understanding of time series, phase portraits, chaotic behaviour, and the equation's sensitivity analysis to external disturbances.