Abstract
In this paper, we firstly investigate the successive applications of three elementary gauge transformation operators Ti with i = 1, 2, 3 for the mKP hierarchy in Kupershmidt-Kiso version, and find that the gauge transformation operators Ti can not commute with each other. Then two types of gauge transformation operators TD and TI constructed from Ti are proved that they can commute with each other. In particular, TI is introduced for the first time in the literature. And the successive applications of TD and TI in the form of T(n,k), which is the product of n terms of TD and k terms of TI, are derived in three cases for different n and k. At last, the corresponding successive applications of TD and TI on the eigenfunction Φ, the adjoint eigenfunction Ψ and the tau functions τ0 and τ1 are considered.
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