A new asymptotic behavior of solutions to the Camassa-Holm equation. (English) Zbl 1259.37046
The author considered the Camassa-Holm equation which models the wave motion in shallow water. This shallow water equation appears in the context of hereditary symmetries studied by Fuchssteiner and Fokas as a bi-Hamiltonian generalization of KdV. The authors study an algebraic decay rate of the strong solution to the Camassa-Holm equation in the \(L^{\infty}\)-space. It is proved that the solution decays algebraically with the same exponent as that of the initial data.
Reviewer: Vassilios Rothos (Thessaloniki)
MSC:
| 37L05 | General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 26A12 | Rate of growth of functions, orders of infinity, slowly varying functions |
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