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# Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrodinger Equations with Small Solitary Waves

@inproceedings{David2004AsymptoticSA, title={Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrodinger Equations with Small Solitary Waves}, author={Liana David and Ian B. Strachan and Sarah Gustafson and Kenji Nakanishi and Tai - Peng Tsai}, year={2004} }

- Published 2004

In this paper, we study a class of nonlinear Schrödinger equations (NLS) which admit families of small solitary wave solutions. We consider solutions which are small in the energy space H, and decompose them into solitary wave and dispersive wave components. The goal is to establish the asymptotic stability of the solitary wave and the asymptotic completeness of the dispersive wave. That is, we show that as t → ∞, the solitary wave component converges to a fixed solitary wave, and the… CONTINUE READING

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