Abstract
In this paper, we employ the qualitative analysis method of planar systems and the numerical simulation approach of differential equations to study the peakons (peaked solitary wave solutions) and periodic cusp wave solutions of the CH- γ equation. By using the bifurcation phase portraits of traveling wave system, the general explicit expressions of the two wave solutions are obtained and their planar graphs are simulated. The qualitative analysis results are identical with the numerical simulation results. Some previous results become our special cases.
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