Stability of small periodic waves for the nonlinear Schrödinger equation

  title={Stability of small periodic waves for the nonlinear Schr{\"o}dinger equation},
  author={Thierry Gallay},
The nonlinear Schrödinger equation possesses three distinct six-parameter families of complexvalued quasi-periodic travelling waves, one in the defocusing case and two in the focusing case. All these solutions have the property that their modulus is a periodic function of x−ct for some c ∈ R. In this paper we investigate the stability of the small amplitude travelling waves, both in the defocusing and the focusing case. Our first result shows that these waves are orbitally stable within the… CONTINUE READING
Highly Cited
This paper has 39 citations. REVIEW CITATIONS


Publications citing this paper.
Showing 1-10 of 27 extracted citations


Publications referenced by this paper.
Showing 1-7 of 7 references

Velo . On a class of nonlinear Schrödinger equations . I . The Cauchy problem , general case

  • J. Ginibre, G.
  • J . Funct . Anal .
  • 1979

Methods of Modern Mathematical Physics IV

  • M. Reed, B. Simon
  • Academic Press, New- York
  • 1978

On the stability theory of solitary waves

  • J. L. Bona
  • Proc. Roy. Soc. London Ser. A 344
  • 1975

On the stability of solutions of the non-linear Schrödinger equation

  • G. Rowlands
  • IMA J. Appl. Math. 13
  • 1974

The stability of solitary waves

  • T. Benjamin
  • Proc. Roy. Soc. London Ser. A 328
  • 1972

Nonlinear stability of periodic travelling wave solutions to the Schrödinger and the modified Kortewegde Vries equations

  • J. Angulo Pava.
  • J . Diff . Equations

Stability of cnoidal waves for the focusing nonlinear Schrödinger equation with potential

  • B. Sandstede, A. Yew.

Similar Papers

Loading similar papers…