Abstract
In this paper, a new generalized two-component Camassa–Holm system is derived via the energy variational approach. This system has two parameters which depend on the energy functional. The initial value problem is investigated. The local well-posedness is obtained when the initial density is away from vacuum. Taking advantage of the method of characteristics and the conservation laws, we prove the blow-up criteria. According to the blow-up criteria, we can prove the finite time blow-up result under some suitable condition. Moreover, we give some exact expression of traveling solutions.
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