# On tau functions associated with linear systems

@article{Blower2012OnTF, title={On tau functions associated with linear systems}, author={Gordon Blower and Samantha Lorraine Newsham}, journal={arXiv: Classical Analysis and ODEs}, year={2012} }

\noindent {\bf Abstract} This paper considers the Fredholm determinant $\det (I-\Gamma_x)$ of a Hankel integral operator on $L^2(0, \infty )$ with kernel $\phi (s+t+2x)$, where $\phi$ is a matrix scattering function. The original contribution of the paper is a related operator $R_x$ such that $\det (I-R_x)=\det (I-\Gamma_x)$ and $-dR_x/dx=AR_x+R_xA$ and an associated differential ring. The paper introduces two main classes of linear systems $(-A,B,C)$ for Schr\"odinger's equation $-\psi''+u\psi… CONTINUE READING

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