广义色散Camassa-Holm模型的奇异孤子

引进一类广义色散Camassa-Holm模型，对其做奇异性分析.通过改进的WTC-Kruskal算法，证明该模型在Painlevé意义下可积，得到了它的一组Painlevé-Bcklund系统和Bcklund变换.应用Maple进行代数运算，得到了丰富的规则(regular)孤子和一类奇异(singular)孤子，扭结(kink)孤子,紧孤子(compacton)和反紧孤子(anti-compacton).特别地，推导出一类在扭结孤子的中间区域包含有一列周期尖点(cuspon)波的奇异结构.在这些规则的孤子系统的基础上，对可积广义系统应用Bcklund变换，得到三类奇异孤子，分别是具有驼峰结构的周期爆破波，具有爆破波结构的扭结孤子和紧孤子. 关键词： 广义Camassa-Holm 模型 周期尖点波 紧孤子 周期爆破波

Singular solitons of generalized Camassa-Holm models

In this paper we introduce one type of generalized dispersive Camassa-Holm model and make its singularity analysis. We prove that the model is Painleve integrable by an alternative WTC-Kruskal test and obtain the Painleve-Backlund systems and the Backlund 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 euspon waves in kink solitons, which occur in their central regions. Based on the regular solitonic system, we do Backlund 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 compaeton.