doi: 10.1685/journal.caim.372

Exact solutions to the integrable discrete nonlinear Schrodinger equation under a quasiscalarity condition

Cornelis Van Der Mee, Francesco Demontis

Abstract


In this article we derive explicit solutions of the matrix integrable discrete
nonlinear Schr\"o\-din\-ger equation under a quasiscalarity condition by using
the inverse scattering transform and the Marchenko method. The Marchenko
equation is solved by separation of variables, where the Marchenko kernel is
represented in the form
$$CA^{-(n+j+1)}e^{i\tau(A-A^{-1})^2}B,$$
$(A,B,C)$ being a matrix triplet where $A$ has only eigenvalues of modulus
larger than one. The class of solutions obtained contains the $N$-soliton and
breather solutions as special cases. Unitarity properties of the scattering
matrix are derived.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909