Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology,
Heriot-Watt University, Edinburgh, July 95

A New Integrable Reduction of the Matrix NLS Equation

A.P. Fordy ¹, M.N. Ozer

¹Department of Applied Mathematical Studies and
Centre for Nonlinear Studies,
University of Leeds, Leeds LS2 9JT, UK


In this paper we perform a multiple scales analysis on the coupled KdV systems associated with an energy-dependent Schr\"odinger operator. We derive the corresponding matrix NLS equation, together with the zero-curvature respresentation. This constitutes a new, integrable NLS system. We present a Hamiltonian structure and constants of motion.

We also present the stationary flows of these equations, giving a new integrable generalisation of the Garnier system, having a $2N \times 2N$ Lax matrix.

Conference paper.


Last modified Mon Apr 8 16:24:54 GB-Eire 1996 (DBD)