SeminarsThe direct and inverse scattering for the Camassa-Holm equation
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The Camassa–Holm (CH) equation is a completely integrable equation as a model describing the unidirectional propagation of shallow water waves over a flat bottom. The solution of CH can be constructed through the direct and inverse scattering methods by considering the Lax pair of CH. Moreover, the scattering data is also important when the large time behaviors of solutions are studied by the Riemann-Hilbert problems. The reflectionless of the scattering data is well-studied on the construction of n-solitons of CH. In this talk, we consider an example to construct the initial condition of CH such that the reflection coefficient of the scattering data is non-zero.
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Chueh-Hsin Chang
2013-04-10
13:00:00 - 15:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
The Camassa–Holm (CH) equation is a completely integrable equation as a model describing the unidirectional propagation of shallow water waves over a flat bottom. The solution of CH can be constructed through the direct and inverse scattering methods by considering the Lax pair of CH. Moreover, the scattering data is also important when the large time behaviors of solutions are studied by the Riemann-Hilbert problems. The reflectionless of the scattering data is well-studied on the construction of n-solitons of CH. In this talk, we consider an example to construct the initial condition of CH such that the reflection coefficient of the scattering data is non-zero.