Colliding solitons for the nonlinear Schrodinger equation

Details Colliding solitons for the nonlinear Schrodinger equation Colliding solitons for the nonlinear Schrodinger equation

2008-04-10

arxiv.org/abs/0804.1608v1

Physics

Mathematical Physics

27 pages

Scientific paper

We study the collision of two fast solitons for the nonlinear Schr\"odinger equation in the presence of a spatially adiabatic external potential. For a high initial relative speed $\|v\|$ of the solitons, we show that, up to times of order $\log\|v\|$ after the collision, the solitons preserve their shape (in $L^2$-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external potential, plus error terms due to radiation damping and the extended nature of the solitons. We remark on how to obtain longer time scales under stronger assumptions on the initial condition and the external potential.

Affiliated with

Also associated with

No associations

Rating

Colliding solitons for the nonlinear Schrodinger equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Colliding solitons for the nonlinear Schrodinger equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Colliding solitons for the nonlinear Schrodinger equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-355381