Corpus ID: 18754230

On tau functions associated with linear systems

  title={On tau functions associated with linear systems},
  author={Gordon Blower and Samantha Lorraine Newsham},
  journal={arXiv: Classical Analysis and ODEs},
  • Gordon Blower, Samantha Lorraine Newsham
  • Published 2012
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • \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