The redistribution of conserved quantities among colliding solitons of the nonlinear Schrödinger equation is considered. An analogy with the theory of spatial solitons in nonlinear optics provides one way to calculate this redistribution. In this context, exchanges of conserved quantities among $N$ colliding solitons can be completely described from a knowledge of the case for $N=2\mathrm{}$. It is shown that solitons generally exchange $L^2$ norm as they collide, with the fraction shared being small when the solitons differ significantly in velocity or amplitude. Exchanges of other conserved densities are also considered.

• Received 28 July 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.38