We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane ...We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.展开更多
In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double d...In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.展开更多
In this paper, the invariant subspaces of the generalized strongly dispersive DGH equation are given, and the exact solutions of the strongly dispersive DGH equation are obtained. Firstly, transform nonlinear partial ...In this paper, the invariant subspaces of the generalized strongly dispersive DGH equation are given, and the exact solutions of the strongly dispersive DGH equation are obtained. Firstly, transform nonlinear partial differential Equation (PDE) into ordinary differential Equation (ODE) systems by using the invariant subspace method. Secondly, combining with the dynamical system method, we use the invariant subspaces which have been obtained to construct the exact solutions of the equation. In the end, the figures of the exact solutions are given.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11361069 and 11775146).
文摘We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.
文摘In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.
文摘In this paper, the invariant subspaces of the generalized strongly dispersive DGH equation are given, and the exact solutions of the strongly dispersive DGH equation are obtained. Firstly, transform nonlinear partial differential Equation (PDE) into ordinary differential Equation (ODE) systems by using the invariant subspace method. Secondly, combining with the dynamical system method, we use the invariant subspaces which have been obtained to construct the exact solutions of the equation. In the end, the figures of the exact solutions are given.
