Breathing patterns in nonlinear relaxation

Details Breathing patterns in nonlinear relaxation Breathing patterns in nonlinear relaxation

2008-09-10

arxiv.org/abs/0809.1842v1

Mathematics

Analysis of PDEs

Scientific paper

In numerical experiments involving nonlinear solitary waves propagating through nonhomogeneous media one observes "breathing" in the sense of the amplitude of the wave going up and down on a much faster scale than the motion of the wave. In this paper we investigate this phenomenon in the simplest case of stationary waves in which the evolution corresponds to relaxation to a nonlinear ground state. The particular model is the popular $ \delta_0 $ impurity in the cubic nonlinear Schroedinger equation on the line. We give asymptotics of the amplitude on a finite but relevant time interval and show their remarkable agreement with numerical experiments. We stress the nonlinear origin of the "breathing patterns" caused by the selection of the ground state depending on the initial data, and by the non-normality of the linearized operator.

Affiliated with

Also associated with

No associations

Rating

Breathing patterns in nonlinear relaxation 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 Breathing patterns in nonlinear relaxation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Breathing patterns in nonlinear relaxation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-161908