Calogero-Moser-Sutherland Dynamical Systems Associated with Nonlocal Nonlinear Schrödinger Equation for Envelope Waves

Abstract

The properties of the soliton and periodic wave solutions of a nonlocal nonlinear Schrödinger equation for envelope waves are investigated by the pole expansion method. For both solutions, the dynamics of the poles are shown to be described by the first-order systems of nonlinear ordinary differential equations (ODEs). A significant result reported here is that in the case of solitons, the system is reducible to the Calogero-Moser dynamical system whereas in the case of periodic waves, the corresponding system is found to be the Calogero-Moser-Sutherland dynamical system. We then establish a purely algebraic method for solving the first-order systems of ODEs and prove their complete integrability.