## The Discrete Self-Trapping Equation

The equation

where
is a complex **n**-vector,
and **M** is a real
symmetric matrix, is known as the Discrete Self-Trapping (DST)
Equation. See J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Physica
D, **16**, 318-338, 1985, for details. In the cases where **M**
is tri-diagonal with constant coefficients, this reduces to a
discrete form of the Nonlinear Schrödinger (DNLS) equation.
A survey concentrating
on the quantized version of the DST equation will be
found in A. C. Scott, J. C. Eilbeck and H. Gilhoj, * Quantum lattice
solitons*, Physica D ** 78**, 194-213, 1994.

A bibliography file dst.pdf on this equation, is
available. Alternatively, download the file dst.tex
and the accompanying .bib file dst.bib and process
these using LaTeX and BibTeX.

Here you will find some of my older
papers on this topic published in obscure conference proceedings which
are now difficult to obtain.

Chris Eilbeck /
Heriot-Watt University / chris@ma.hw.ac.uk / tel. +44 (0)131 451
3220