In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.
GUO Boling & LIU Zhengrong Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
In this paper, we investigate the number, location and stability of limit cycles in a class of perturbed polynomial systems with (2n+1) or (2n+2)-degree by constructing detection function and using qualitative analysis. We show that there are at most n limit cycles in the perturbed polynomial system, which is similar to the result of Perko in [8] by using Melnikov method. For n=2, we establish the general conditions depending on polynomial's coefficients for the bifurcation location and stability of limit cycles. The bifurcation parameter value of limit cycles in [5] is also improved by us. When n=3 the sufficient and necessary conditions for the appearance of 3 limit cycles are given. Two numerical examples for the location and stability of limit cycles are used to demonstrate our theoretical results.
In this paper the qualitative analysis methods of planar autonomous systems and numerical simu-lation are used to investigate the peaked wave solutions of CH-r equation. Some explicit expressions of peakedsolitary wave solutions and peaked periodic wave solutions are obtained, and some of their relationships arerevealed. Why peaked points are generated is discussed.
