B-Class Solitary Wave And Their Persistence Under KURAMOTO-SIVASHINSKY Perturbation

In this paper,the main object of study is the b-class shallow water equation 8)+ 26) + (78) + 8)= 0, ∈ , > 0,where (7 and 6)are arbitrary real constants with momentum density 8)= -.In the first part of this paper,we take (7 and 6)separately as the bifurcation parameters to study the existence of solitary wave solutions of b-class equation and correspondingly we achieve some corollaries.In the second part of this paper,based on the results we already achieved,we study the persistence of solitary wave solutions under singular Kuramoto-Sivashinsky perturbation.The main analysis methods are the qualitative theory of differential equations,the bifurcation theory of dynamical systems and the geometric singular perturbation theory.