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# Stability of small periodic waves for the nonlinear Schrödinger equation

@inproceedings{Gallay1979StabilityOS, title={Stability of small periodic waves for the nonlinear Schr{\"o}dinger equation}, author={Thierry Gallay}, year={1979} }

- Published 1979

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