CONNECTION BETWEEN SOLITONS AND GEOMETRIC PHASES

The connection between moving space curves and soliton dynamics is exploited to show that soliton-supporting systems of a certain class are naturally endowed with a geometric phase density. The phase information is contained in the Lax pair structure associated with soliton evolution. The vanishing of the global (integrated) phase is shown to lead to an infinite number of conserved densities. Explicit expressions for the phase density are given for the modified Korteweg-de Vries, non-linear Schrodinger and sine-Gordon equations.