| Abstract: |
| The Cauchy problem of a third-order dispersive Camassa-Holm equation with cubic nonlinearities having initial data $\varphi(x)$ in analytic spaces is studied. First, local well-posedness in analytic Gevrey spaces, is established by using trilinear estimates in analytic Bourgain spaces. Then, using the fact that solution of this equation conserve their $H^1$-norm, an almost conservation law in the corresponding analytic Gevrey spaces is derived. |
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