On the Cauchy problem for the Camassa-Holm equation. (English) Zbl 0980.35150

From the introduction: We study local and global well-posedness with respect to the real-valued solutions of the Cauchy problem associated to the Camassa-Holm equation \[ u_t- u_{xxt}+ 3uu_x= 2u_x u_{xx}+ u_{xxx},\quad x\in \mathbb{R},\;t\in \mathbb{R}, \] that was derived recently as a new model for dispersive shallow water waves.


35Q53 KdV equations (Korteweg-de Vries equations)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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