Global dissipative solutions of a modified two-component Camassa-Holm shallow water system

By introducing a new set of independent variables, we first transform a modified two-component Camassa-Holm shallow water system into a semilinear system. To obtain a dissipative solution, we modify the corresponding system into a discontinuous system. Then we map the solution of system to the dissipative solution of original equation. Moreover we prove that these global dissipative solutions construct a semigroup. (C) 2011 American Institute of Physics. [doi:10.1063/1.3562928]