In this article, we study the self-similar solutions of the 2-component Camassa–Holm equations , , with . By the separation method, we can obtain a class of blowup or global solutions for or −1. In particular, for the integrable system with , we have the global solutions, for , for , , , , where with ; and are arbitrary constants. Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.
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