Zhang, Pingzheng; Liu, Yue Stability of solitary waves and wave-breaking phenomena for the two-component Camassa-Holm system. (English) Zbl 1231.35184 Int. Math. Res. Not. 2010, No. 11, 1981-2021 (2010). Summary: Considered herein is a two-component Camassa-Holm system modeling shallow water waves moving over a linear shear flow. It is shown here that solitary-wave solutions of the system are dynamically stable to perturbations for a range of their speeds. On the other hand, a new wave-breaking criterion for solutions is established, and two results of wave-breaking solutions with certain initial profiles are described in detail. Moreover, a sufficient condition for global solutions determined only by a nonzero initial profile of the free surface component of the system is found. Cited in 48 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35B35 Stability in context of PDEs 35C08 Soliton solutions 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction PDFBibTeX XMLCite \textit{P. Zhang} and \textit{Y. Liu}, Int. Math. Res. Not. 2010, No. 11, 1981--2021 (2010; Zbl 1231.35184) Full Text: DOI Link