Solving the constrained modified KP hierarchy by gauge transformations

Abstract

In this paper, we mainly investigate two kinds of gauge transformations for the constrained modified KP hierarchy in Kupershmidt-Kiso version. The corresponding gauge transformations are required to keep not only the Lax equation but also the Lax operator. For this, by selecting the special generating eigenfunction and adjoint eigenfunction, the elementary gauge transformation operators of modified KP hierarchy \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T_D}(\\Phi ) = ({\\Phi ^{ - 1}})_x^{ - 1}\\partial {\\Phi ^{ - 1}}$$\\end{document} and TI(Ψ) = Ψ−1∂−1Ψx, become the ones in the constrained case. Finally, the corresponding successive applications of TD and TI on the eigenfunction Φ and the adjoint eigenfunction Ψ are discussed.