Lax formulation of 3--component KP hierarchy by Shiota construction
It is quite basic in integrable systems to deriving Lax equations from bilinear equations. For multi--component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators $Λ_1$ and $Λ_2$, where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases.
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