  In this paper, we establish local well-posedness of the Cauchy problem for a
recently proposed dispersion generalized Camassa-Holm equation by using Kato's
semigroup approach for quasi-linear evolution equations. We show that for
initial data in the Sobolev space $H^{s}(\mathbb{R})$ with $s>\frac{7}{2}+p$,
the Cauchy problem is locally well-posed, where $p$ is an even real number
determined by the order of the positive differential operator $L$ corresponding
to the dispersive effect added to the Camassa-Holm equation.
