Summary: ``Nonlinear dynamics of the damped driven sine-Gordon equation $$u_{tt}-u_{xx}+\sin u=-\epsilon(\alpha u_t-\Gamma\cos\omega t)$$ where $0<\epsilon\ll1,\alpha,\Gamma>0$, with even spatial symmetry and periodic boundary conditions $$u(L/2,t)=u(-L/2,t),\ u(x,t)=u(-x,t),$$ has been studied extensively by numerical and analytical methods, because it is a typical model for the study of chaotic attractors in infinite-dimensional dynamical systems. However, there has not been any rigorous proof on some interesting dynamics of this model, such as the chaotic jumping behavior in time with spatial coherence. In this paper, the dynamics mechanism of the phenomenon is investigated analytically. First, based on an idea of the generalized asymptotic inertial manifold (GAIM) of the dissipative partial differential equation (PDE), a four-dimensional first-order ordinary differential equation (ODE) is derived by restricting the above PDE to its GAIM, which is a perturbed near-integrable Hamiltonian system with a certain resonance. Then the ODE is studied qualitatively by the singular perturbation theory. Without any artificial conditions, an analytical criterion for the existence of Shilʹnikov-type orbits homoclinic to the resonant band is obtained. In comparison with the previous results, these results are more coincident with the physical facts. However, such a criterion does not hold completely under the parametric values specified in the previous numerical experiments, and it is indicated that other orbits homoclinic (or heteroclinic) to the resonant band probably exist. Then under these parametric values, it is shown that there exist at least four stable structurally pulse-orbits, which are numerically observable, connecting a saddle-saddle-type equilibrium to a saddle-focus-type equilibrium in the resonant band by applying the method proposed by Haller and Wiggins. This explains the chaotic jumping behavior observed by the numerical experiments.''