On the energy exchange between resonant modes in nonlinear Schrödinger equations

Details On the energy exchange between resonant modes in nonlinear Schrödinger equations On the energy exchange between resonant modes in nonlinear Schrödinger equations

2010-08-20

arxiv.org/abs/1008.3527v1

Mathematics

Dynamical Systems

Scientific paper

We consider the nonlinear Schr\"odinger equation $$ i\psi_t= -\psi_{xx}\pm 2\cos 2x \ |\psi|^2\psi,\quad x\in S^1,\ t\in \R$$ and we prove that the solution of this equation, with small initial datum $\psi_0=\e (\cos x+\sin x)$, will periodically exchange energy between the Fourier modes $e^{ix}$ and $e^{-ix}$. This beating effect is described up to time of order $\e^{-9/4}$ while the frequency is of order $\e^2$. We also discuss some generalizations.

Affiliated with

Also associated with

No associations

Rating

On the energy exchange between resonant modes in nonlinear Schrödinger equations 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 On the energy exchange between resonant modes in nonlinear Schrödinger equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the energy exchange between resonant modes in nonlinear Schrödinger equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-81198