In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system: * E-mail address: nevetsyuen@hotmail.com 2 M.W. Yuen stabilities of numerical methods for the systems. With the characteristic line method, blowup phenomenon for k3 ≥ 0 is also studied. Mathematics Subject Classification (2010): 35B40, 35B44, 35C06, 35Q53