Abstract
In this paper, the (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation is studied by the bifurcation theory of dynamical system. Based on this theory, phase portraits of different topological structures of the equation are obtained, which clearly show all bounded orbits corresponding to the bounded traveling waves of the equation. Furthermore, the periodic wave solution of the (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation are obtained by calculating complicated elliptic integrals.
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