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Traveling waves of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation
Lan Wang,Yuqian Zhou,Qian Liu,Qiuyan Zhang
Keywords:KP-Boussinesq equation, traveling waves, bifurcation, dynamical system
      In this paper, the bifurcation theory of dynamical system is applied to study the traveling waves of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq (KP-Boussinesq) equation. Parameter bifurcation sets are derived to divide the parameter space into three regions in which qualitatively different phase portraits are given. Based on them, all bounded and unbounded orbits are identified clearly. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all single wave solutions of the (3+1)-dimensional KP-Boussines equation without any loss.