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arXiv · 2110.01492

Asymptotic stability of solitary waves for the 1D cubic-quintic Schr\"odinger equation with no internal mode

Yvan Martel
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Abstract

For the Schr\"odinger equation with a cubic-quintic, focusing-defocusing nonlinearity in one space dimension, we prove the asymptotic stability of solitary waves for a large range of admissible frequencies. For this model, the linearized problem around the solitary waves does not have internal mode nor resonance.

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Yvan Martel. 2021-10-04. Asymptotic stability of solitary waves for the 1D cubic-quintic Schr\"odinger equation with no internal mode. https://doi.org/10.2140/pmp.2022.3.839

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