Academic Journal
A higher-order quadratic NLS equation on the half-line.
| العنوان: | A higher-order quadratic NLS equation on the half-line. |
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| المؤلفون: | Himonas, A Alexandrou, Yan, Fangchi |
| المصدر: | J Evol Equ ; ISSN:1424-3202 ; Volume:25 ; Issue:1 |
| سنة النشر: | 2025 |
| المجموعة: | PubMed Central (PMC) |
| مصطلحات موضوعية: | Fokas unified transform method, Higher-order nonlinear Schrödinger equation, Initial-boundary value problem on the half-line, Linear and bilinear estimates in Bourgain spaces, Quadratic nonlinearities, Well-posedness in Sobolev spaces |
| الوصف: | The well-posedness of the initial-boundary value problem for higher-order quadratic nonlinear Schrödinger equations on the half-line is studied by utilizing the Fokas solution formula for the corresponding linear problem. Using this formula, linear estimates are derived in Bourgain spaces for initial data in spatial Sobolev spaces on the half-line and boundary data in temporal Sobolev spaces suggested by the time regularity of the linear initial value problem. Then, the needed bilinear estimates are derived and used for showing that the iteration map defined via the Fokas solution formula is a contraction in appropriate solution spaces. Finally, well-posedness is established for optimal Sobolev exponents in a way analogous to the case of the initial value problem on the whole line with solutions in classical Bourgain spaces. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | https://doi.org/10.1007/s00028-024-01034-w; https://pubmed.ncbi.nlm.nih.gov/39691164; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646971/ |
| DOI: | 10.1007/s00028-024-01034-w |
| الاتاحة: | https://doi.org/10.1007/s00028-024-01034-w https://pubmed.ncbi.nlm.nih.gov/39691164 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646971/ |
| Rights: | © The Author(s) 2024. |
| رقم الانضمام: | edsbas.6906C095 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/s00028-024-01034-w |
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