In this paper we study the transfer of information between colliding solitary waves. By this we mean the following: The state of a solitary wave is a set of parameters, such as amplitude, width, velocity, or phase, that can change during collisions. We say information is transferred during a collision of solitary waves $A$ and $B$ if the state of $B$ after the collision depends on the state of $A$ before the collision. This is not the case in the cubic nonlinear Schrödinger, Korteweg–de Vries, and many other integrable systems. We show by numerical simulation that information can be transferred during collisions in the (nonintegrable) saturable nonlinear Schrödinger equation. A seemingly complementary feature of collisions in this and similar systems is radiation of energy. We give results that show that significant information can be transferred with radiation no greater than a few percent. We also discuss physical realization using recently described spatial solitary light waves in a saturable glass medium.

• Received 28 February 1997

DOI:https://doi.org/10.1103/PhysRevE.56.7267