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New bounded traveling waves of Camassa-Holm equation. (English) Zbl 1063.35138

Summary: The bifurcation method of planar systems and simulation method of differential equations are employed to investigate the bounded traveling waves of the Camassa-Holm equation. Some new bounded traveling waves are found and their implicit expressions are obtained. Both qualitative and numerical results show that they possess the properties of compactons or generalized kink waves.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
34A05 Explicit solutions, first integrals of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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