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arXiv · 1709.00586

Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one

Daniele Garrisi·Vladimir Georgiev
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Abstract

We show that symmetric and positive profiles of ground-state standing-wave of the non-linear Schrödinger equation are non-degenerate and unique up to a translation of the argument and multiplication by complex numbers in the unit sphere. The non-linear term is a combination of two or three pure-powers. The class of non-linearities satisfying the mentioned properties can be extended beyond two or three power combinations. Specifically, it is sufficient that an Euler differential inequality is satisfied and that a certain auxiliary function is such that the first local maximum is also an absolute maximum.

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Daniele Garrisi, Vladimir Georgiev. 2017-09-02. Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one. https://arxiv.org/abs/1709.00586

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