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.