The trajectories of interacting self-guided beams in a homogeneous nonlinear medium are derived directly from the Lorentz force of classical electromagnetic theory, treating the beams as particles with mass. This, to our knowledge, is the first self-consistent particle description of beam interaction, and, in particular, one that does not rely upon interpretation of the wave equation. The method is applicable to any stable beams, in both two and three dimensions.

• Received 18 December 1995

DOI:https://doi.org/10.1103/PhysRevLett.77.271