Abstract
The bifurcation method of dynamical system is applied to study traveling waves of the Joseph—Egri equation. The phase space geometry of traveling wave system of the Joseph—Egri equation is investigated in detail. We obtain the parameter bifurcation sets in which various bounded and unbounded orbits are identified and simulated. Furthermore, by the calculation of complicated elliptic integrals, exact expressions of all traveling wave solutions of the Joseph—Egri equation are given, including bounded and unbounded ones.
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