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Compacton-like wave and kink-like wave of GCH equation. (English) Zbl 1106.35065

Summary: We combine qualitative analysis with numerical exploration to study traveling waves of a generalized Camassa–Holm equation. Two new types of bounded traveling waves are found. One of them is called compacton-like wave because it is of some properties of compacton. Similarly, the other is called kink-like wave since it possesses some properties of kink. Their implicit expressions are obtained. For some concrete data, the diagrams of the implicit functions are displayed, and the numerical simulation is made. The results imply that our theoretical analysis is agreeable with the numerical simulation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35C07 Traveling wave solutions
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