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

### Abstract

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.

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