On Asymptotic Stability of Ground States of Nls with a Finite Bands Periodic Potential in 1 D

@inproceedings{Cuccagna2009OnAS,
  title={On Asymptotic Stability of Ground States of Nls with a Finite Bands Periodic Potential in 1 D},
  author={Scipio Cuccagna and N. Visciglia},
  year={2009}
}
We consider a nonlinear Schrödinger equation iut − h0u+ β(|u|)u = 0 , (t, x) ∈ R× R, with h0 = − d 2 dx2 + P (x) a Schrödinger operator with finitely many spectral bands. We assume the existence of an orbitally stable family of ground states. Exploiting dispersive estimates in Cuccagna (2008), Cuccagna and Visciglia (2009), and following the argument in Cuccagna (to appear) we prove that under appropriate hypotheses the ground states are asymptotically stable. 

References

Publications referenced by this paper.
Showing 1-10 of 26 references

Time decay of finite energy solutions of the nonlinear Klein Gordon and Schrödinger equations

G. Velo Ginibre
J . Diff . Equations • 2007

Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein – Gordon equations

H. T. Yau Tsai
Nonlinearity • 2005

I.M.Sigal, Asymptotic stability of nonlinear Schrödinger equations with potential

Zhou Gang
Rev. Math. Phys • 2005

Spectra of positive and negative energies in the linearization of the NLS problem

N. Visciglia Cuccagna
Comm . Pure Appl . Math . • 2005

Stability of solitary waves in the presence of symmetries

J. Shatah Grillakis, W. Strauss
Rev . Math . Phys . • 2005

Similar Papers

Loading similar papers…