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.