Abstract: The mathematical modeling of important phenomena arising in physics and biology often leads to nonlinear wave equations. It is quite remarkable that many of these universal equations exhibit a regular behavior, typical of integrable partial differential systems (there exist Hamiltonian structures). And their traveling wave systems are also integrable ordinary differential equations, in which there exist some singular properties. In this talk, we introduce the dynamical behavior for the singular traveling wave systems of the second class. As examples, for some very interesting mathematical models which describe specific natural phenomena, we study the bifurcations and exact solutions of given systems.