Center stable manifold for ground states of nonlinear Schr\"odinger equations with internal modes

Masaya Maeda; Yohei Yamazaki

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arXiv · 2206.08156

Center stable manifold for ground states of nonlinear Schr\"odinger equations with internal modes

Masaya Maeda·Yohei Yamazaki

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Abstract

We study the dynamics of solutions of nonlinear Schr\"odinger equation near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is proved. The novelty of our result is that we allow the existence of internal modes.

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Masaya Maeda, Yohei Yamazaki. 2022-06-16. Center stable manifold for ground states of nonlinear Schr\"odinger equations with internal modes. https://arxiv.org/abs/2206.08156

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