Bifurcation analysis and exact solutions of the conformable time fractional Symmetric Regularized Long Wave equation

Abstract

This paper investigates exact solutions for the conformable time fractional Symmetric Regularized Long Wave equation by applying the bifurcation analysis method and the exp(−Φ(ξ))-expansion method. By analyzing the long behaviors of the exact solutions plotted in 3D and 2D figures, we can model weakly nonlinear ion acoustic and space-charge waves. The bifurcation of the equation is analyzed based on the condition where the first integral constant is zero and the second integral constant is not zero. Based on different parameter conditions, many phase portraits and exact solutions including dark soliton, bright soliton, breaking wave, periodic and singular solutions for the equation are obtained. It has been proven that bifurcation method provides a wider range of solutions compared with other methods. Then the exp(−Φ(ξ))−expansion method is utilized to get the more solutions. Next graphical representations are presented that show physical characteristics of the solutions and the significance of the methods for fractional partial differential equations. Finally, we make a comprehensive comparison with other literatures.