Do Solitons Exchange Conserved Quantities During Collisions?
P. D. Miller and N. N. Akhmediev
Optical Sciences Centre
Research School of Physical Sciences and Engineering
The Australian National University, Canberra ACT 0200 Australia
Abstract:
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. It is shown that solitons generally exchange L2 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.