The gauge transformation of the constrained semi-discrete KP hierarchy

TL;DR

This paper explicitly constructs gauge transformations for the constrained semi-discrete KP hierarchy, providing formulas for transformed eigenfunctions and tau-functions, advancing understanding of integrable systems.

Contribution

It introduces a method to explicitly perform gauge transformations on the constrained semi-discrete KP hierarchy, including formulas for eigenfunctions and tau-functions.

Findings

Explicit formulas for gauge transformations in cdKP hierarchy

Transformed eigenfunctions and tau-functions derived

Advances in integrable systems theory

Abstract

In this paper, the gauge transformation of the constrained semi-discrete KP(cdKP) hierarchy is constructed explicitly by the suitable choice of the generating functions. Under the $m$-step successive gauge transformation $T_m$, we give the transformed (adjoint) eigenfunctions and the $\tau$-function of the transformed Lax operator of the cdKP hierarchy.