Abstract
<abstract> In this paper, the bifurcation theory of dynamical system is applied to study traveling waves of two types of generalized breaking soliton (GBS) equations which include many famous partial differential equation models. Without any parameter constraints, we investigate their traveling wave systems in detail from the geometric point of view. Due to the existence of a two dimensional invariant manifold, all bounded and unbounded orbits are identified and studied in different parameter bifurcation sets. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all possible single wave solutions of two types of GBS equations. </abstract>
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