LOCAL DYNAMICS NEAR UNSTABLE BRANCHES OF NLS SOLITONS

@inproceedings{Combet2013LOCALDN,
  title={LOCAL DYNAMICS NEAR UNSTABLE BRANCHES OF NLS SOLITONS},
  author={Vianney Combet and Tai-Peng Tsai and Ian Zwiers},
  year={2013}
}
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, solutions to initial data from a neighbourhood of the branch either converge to a soliton, or exit a larger neighbourhood of the branch transversally. The qualitative dynamic near a branch of unstable solitons is irrespective of whether blowup eventually occurs, which has practical implications for… CONTINUE READING

Similar Papers

Figures and Topics from this paper.

References

Publications referenced by this paper.
SHOWING 1-10 OF 43 REFERENCES

On the stability of solitary waves for nonlinear Schrödinger equations

V. Buslaev, G. Perelman
  • American Mathematical Society Translations,
  • 1995
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Mızrak. Asymptotic stability of ground states in 3D nonlinear Schrödinger equation including subcritical cases

Ö.E. Kirr
  • Journal of Functional Analysis,
  • 2009
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Mızrak. On the stability of ground states in 4D and 5D nonlinear Schrödinger equation including subcritical cases

Ö.E. Kirr
  • http://arxiv.org/abs/0906.3732, preprint,
  • 2009
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL