Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains

Details Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains

2011-03-31

arxiv.org/abs/1103.6202v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

We analyze the 1D focusing nonlinear Schr\"{o}dinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally these equations elucidate the unique role of the zero mode for the Neumann boundary conditions.

Affiliated with

Also associated with

No associations

Rating

Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains 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 Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245659