The Construction Of Solutions To(3+1) Dimensional Space-time Fractional MKdV-ZK Equation And Modified Nonlinear Schr?dinger Equation

(3+1)dimensional space-time fractional mKdV-ZK equation is studied by bifurcation theory of dynamical systems and polynomial complete discriminant system method.The modified nonlinear Schr?dinger equation is studied by auxiliary differential equation method.The main research objects,methods and results are as follows:1.(3+1)dimensional space-time fractional mKdV-ZK equation is transformed into a planar dynamic system.Then,with the help of bifurcation theory of dynamical system,the bifurcation phase diagrams under different conditions are obtained.Finally,according to the bifurcated phase diagrams,different evolution orbits are given and integrated along the orbits.A series of exact solutions of(3+1)dimensional space-time fractional mKdV-ZK equation are constructed,including four new solutions.2.(3+1)dimensional space-time fractional mKdV-ZK equation is transformed into an elementary integral form.The polynomial roots in the integrand function are classified and discussed by using the quadric polynomial complete discriminant system,and a series of exact solutions are obtained,including four new solutions.3.Modified nonlinear Schr?dinger equation is transformed into an ordinary differential equation.Then,the solution of ordinary differential equation is obtained by using the auxiliary differential equation method.Finally,some explicit exact solutions of modified nonlinear Schr?dinger equation are obtained,including four new solutions.