The gauge transformation of the modified KP hierarchy

DOI

10.1080/14029251.2018.1440743How to use a DOI?

Keywords

mKP hierarchy; gauge transformation; tau function

Abstract

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

Copyright

© 2018 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Jipeng Cheng
PY  - 2021
DA  - 2021/01/06
TI  - The gauge transformation of the modified KP hierarchy
JO  - Journal of Nonlinear Mathematical Physics
SP  - 66
EP  - 85
VL  - 25
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1440743
DO  - 10.1080/14029251.2018.1440743
ID  - Cheng2021
ER  -