Bifurcation, chaotic, variational principle and new soliton solutions for the nonlinear fractional Drinfeld-Sokolov system

In this work, the nonlinear fractional Drinfeld-Sokolov system is explored with conformable fractional derivative. The fractional travelling wave transformation and Galilean transformation are employed to convert the nonlinear fractional Drinfeld-Sokolov system into a planar dynamical, and its bifurcation and chaotic analysis are made, which are elaborated by displaying 3D and 2D phase portraits . The variational principle of the nonlinear fractional Drinfeld-Sokolov system is successfully established via semi-inverse method, which is particularly helpful for a deeper understanding of the structure and conservation laws of the solutions . Bright soliton and periodic solutions are also obtained based on the variational principle. Finally, the unified solver method and (P/Q)-expansion method are successfully adopted to derive some new soliton solutions. The dynamic behaviour of these acquired new solutions are depicted by using corresponding 3D,contour, density and 2D graphs with various parameter choices.