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On the multipeakon dissipative behavior of the modified coupled Camassa-Holm model for shallow water system. (English) Zbl 1296.76019
Summary: This paper investigates the multipeakon dissipative behavior of the modified coupled two-component Camassa-Holm system arisen from shallow water waves moving. To tackle this problem, we convert the original partial differential equations into a set of new differential equations by using skillfully defined characteristic and variables. Such treatment allows for the construction of the multipeakon solutions for the system. The peakon-antipeakon collisions as well as the dissipative behavior (energy loss) after wave breaking are closely examined. The results obtained herein are deemed valuable for understanding the inherent dynamic behavior of shallow water wave breaking.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35Q35 PDEs in connection with fluid mechanics
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