NLS ground states on graphs
By R. Adami, E. Serra, Paolo Tilli. 2014
140 citations recorded by the source corpus.
We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the assumption is not fulfilled and ground states actually exist. In order to obtain the result, we introduce a new rearrangement technique, adapted to the graph where it applies. Owing to such a technique, the energy level of the rearranged function is improved by conveniently mixing the symmetric and monotone rearrangement procedures.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a796b8ce36511fa1493d077162dc2dc65dc03a19
How researchers see this paper
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
- Simone Dovetta
- Louis Jeanjean
- Nicola Soave
- Xiaojun Chang
- E. Serra
- Lorenzo Tentarelli
- Thomas Bartsch
- Xinfu Li
In Statistical and Nonlinear Physics
- Simone Dovetta
- Louis Jeanjean
- Xiaojun Chang
- Nicola Soave
- E. Serra
- Lorenzo Tentarelli
- Xinfu Li
- Thomas Bartsch
Citations in the corpus
- Bound states of the NLS equation on metric graphs with localized nonlinearities (2015, background): “2 Functional setting We start by recalling briefly some basic facts and defintions concerning metric graphs (for a modern account on the topic we refer the reader to [20, 9, 3] and references therein).”
- Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs (2022, background): “In such frameworks, a particularly relevant issue concerns the existence of ground states, that is, global minimizers of the energy under the mass constraint, see [2, 3, 4, 5] for non-compact G , and [11, 12] for the compact case.”
- Existence of infinite stationary solutions of the $L^2$-subcritical and critical NLSE on compact metric graphs (2017, background): “nsider a non-constant function u. Replacing uwith |u|, we may assume u>0. Let ℓ:= |G| be the total length of G. Considering the decreasing rearrangement u∗ of uon [0,ℓ), it is well-known (see e.g. [5]) that u∗ ∈ H1 µ(0,ℓ), u∗ is non-increasing on [0,ℓ] and ku∗k L6(0,ℓ) = kukL6(G) k(u∗)′k L2(0,ℓ) ”