Bifurcation Analysis and Travelling Wave Solution for a Generalized Time Fractional KdV Equation

Abstract

By using bifurcation theory of planar dynamic system to a generalized time fractional KdV equation, a large number of solutions including irrational function solution, Jacobian elliptic function solution, trigonometric function solution, solitary solution as well as compacton solution are derived. Under different parametric selection, various kinds of sufficient conditions and numerical simulations are demonstrated to visualize their mechanism.