On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue
We prove in dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/24/3876 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850060043549933568 |
|---|---|
| author | Scipio Cuccagna Masaya Maeda |
| author_facet | Scipio Cuccagna Masaya Maeda |
| author_sort | Scipio Cuccagna |
| collection | DOAJ |
| description | We prove in dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> a result similar to a classical paper by Soffer and Weinstein, Jour. Diff. Eq. 98 (1992), improving it by encompassing for pure power nonlinearities the whole range of exponents <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008). |
| format | Article |
| id | doaj-art-cbc3c286ee2541ad9772edde414812d3 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cbc3c286ee2541ad9772edde414812d32025-08-20T02:50:41ZengMDPI AGMathematics2227-73902024-12-011224387610.3390/math12243876On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single EigenvalueScipio Cuccagna0Masaya Maeda1Department of Mathematics, Informatics and Geosciences, University of Trieste, Via Valerio 12/1, 34127 Trieste, ItalyDepartment of Mathematics and Informatics, Graduate School of Science, Chiba University, Chiba 263-8522, JapanWe prove in dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> a result similar to a classical paper by Soffer and Weinstein, Jour. Diff. Eq. 98 (1992), improving it by encompassing for pure power nonlinearities the whole range of exponents <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008).https://www.mdpi.com/2227-7390/12/24/3876nonlinear Schödinger equationasymptotic stabilityground state |
| spellingShingle | Scipio Cuccagna Masaya Maeda On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue Mathematics nonlinear Schödinger equation asymptotic stability ground state |
| title | On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue |
| title_full | On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue |
| title_fullStr | On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue |
| title_full_unstemmed | On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue |
| title_short | On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue |
| title_sort | on small energy solutions of the nonlinear schrodinger equation in 1d with a generic trapping potential with a single eigenvalue |
| topic | nonlinear Schödinger equation asymptotic stability ground state |
| url | https://www.mdpi.com/2227-7390/12/24/3876 |
| work_keys_str_mv | AT scipiocuccagna onsmallenergysolutionsofthenonlinearschrodingerequationin1dwithagenerictrappingpotentialwithasingleeigenvalue AT masayamaeda onsmallenergysolutionsofthenonlinearschrodingerequationin1dwithagenerictrappingpotentialwithasingleeigenvalue |