| The traveling wave solutions are one of the most important solutions in the partial differential equations.The traveling wave solutions of the partial differential equations are solutions of the form u(x,t)=u(z)=u(x-ct),z=x-ct,where the wave velocity c is a constant and the function u(z)propagates with constant c along a fixed direction of the independent variable.The traveling wave solutions are a steady state solution of the partial differential equations,with some characteristics such as propagation speed,stability,etc.Many phenomena in real life can be described by the traveling wave solutions.In this paper,the following three models are studied for the dynamic properties of traveling wave solutions:In first part,this paper is to investigate the influence of the cutoff to the minimal wave speed of the traveling wave solutions for the Fitzhugh-Nagumo equation.Through the smooth matching of the traveling wave solutions from three different boundary layers,we obtained the explicit expression of Ac which is relate to the parameter ε.In second part,the speed selection of the time periodic traveling wave for a three species time-periodic Lotka-Volterra competition system is studied via the upper-lower solutions method as well as the comparison principle.Through constructing specific types of upper and lower solutions to the system,the speed selection of the minimal wave speed can be determined under some sets of sufficient conditions composed of the parameters in the system.In third part,the bifurcation of the traveling wave solutions of the Novikov equation in dynamic are discussed.The new Hamiltonian function is established by using the bifurcation method of the dynamic system.We derive all negative solitions,while the case of positive solutions has been studied by Pan.After a series of nonlinear transformations,the parameter expressions of the soliton solutions in different situations are obtained. |
