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

@inproceedings{Garrisi2019UniquenessOS,
  title={Uniqueness of standing-waves for a non-linear Schrodinger equation with three pure-power combinations in dimension one},
  author={Daniele Garrisi and Vladimir Georgiev},
  year={2019}
}
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… CONTINUE READING

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