Abstract： In this paper we introduce one type of generalized dispersive Camassa-Holm model and make its singularity analysis. We prove that the model is Painlevé integrable by an alternative WTC-Kruskal test and obtain the Painlevé-Bcklund systems and the Bcklund transformation. Many new types of regular soliton, singular soliton, kink soliton, compacton and anti-compacton are explored. Particularly, we have found singular structures of periodic cuspon waves in kink solitons, which occur in their central regions. Based on the regular solitonic system, we do Bcklund transformation and obtain three sorts of singular solitons, namely the periodic blow-up wave with hump structure, kink soliton for the blow-up wave structure and the compacton.
generalized Camassa-Holm modelperiodic cuspon wavecompactonperiodic blow-up wave