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arXiv · 2306.13950

The monotonicity conjecture and stability of solitons for the Cubic-Quintic NLS on R^3

Jian Zhang·Shuihui Zhu
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Abstract

In this paper, we prove stability or instability of solitons for the cubic-quintic nonlinear Schrodinger equation at every frequency. The monotonicity conjecture raised by Killip, Oh, Pocovnicu and Visan is resolved. We introduce and solve a new cross-constrained variational problem. Then the uniqueness of the energy minimizers is proposed and shown. According to a spectral approach and variational arguments, we develop a set of geometric analysis methods. Correspondences between the soliton frequency and the prescribed mass are established. Classification of normalized solutions is given.

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Jian Zhang, Shuihui Zhu. 2023-06-24. The monotonicity conjecture and stability of solitons for the Cubic-Quintic NLS on R^3. https://arxiv.org/abs/2306.13950

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