| Abstract: |
| We solve Cauchy problems for some $\mu$-Camassa-Holm integro-partial
differential equations in the analytic category. The equations to
be considered are $\mu$CH of Khesin-Lenells-Misio\l{}ek, $\mu$DP
of Lenells-Misio\l{}ek-Ti\u{g}lay, the higher-order $\mu$CH of Wang-Li-Qiao
and the non-quasilinear version of Qu-Fu-Liu. We prove the unique
local solvability of the Cauchy problems and provide an estimate of
the lifespan of the solutions. Moreover, we show the existence of
a unique global-in-time analytic solution for $\mu$CH, $\mu$DP and
the higher-order $\mu$CH. |
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