Bifurcation Of Traveling Wave Solutions And Dynamical Behaviors Of A Class Of K (m, N) Equations With Generalized Evolution Terms

In this paper, by using bifurcation theory and methods of plane dynamic system, we investigate thebifurcation and dynamical behavior of some special cases of a class of K(m, n) equations, i.e. (ul)t +aumux +(?), n = 2, l≥2. We obtain some exact explicit parametric representations oftraveling wave solutions by using time scaling transformation. We convert K(m, n) equation into a regularsystem, then the bifurcation and dynamical behaviors of regular system is discussed using bifurcation theoryof dynamic system. By discussing regular system, we find the existence of traveling wave solution anddynamical behavior of the singular traveling wave system. Meanwhile we get some exact traveling waveand the existence of periodic solution.