Quadratic Klein-Gordon equations with a potential in one dimension
This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely only on Strichartz or virial estimates and is therefore able to treat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2022-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508622000099/type/journal_article |
| _version_ | 1827994899035717632 |
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| author | Pierre Germain Fabio Pusateri |
| author_facet | Pierre Germain Fabio Pusateri |
| author_sort | Pierre Germain |
| collection | DOAJ |
| description | This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely only on Strichartz or virial estimates and is therefore able to treat low-power nonlinearities (hence also nonlocalised solitons) and capture the global (in space and time) behaviour of solutions. |
| first_indexed | 2024-04-10T04:48:10Z |
| format | Article |
| id | doaj.art-575c7ec779744e0dbc6e667c3f02e286 |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:48:10Z |
| publishDate | 2022-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-575c7ec779744e0dbc6e667c3f02e2862023-03-09T12:34:22ZengCambridge University PressForum of Mathematics, Pi2050-50862022-01-011010.1017/fmp.2022.9Quadratic Klein-Gordon equations with a potential in one dimensionPierre Germain0https://orcid.org/0000-0003-3148-4127Fabio Pusateri1https://orcid.org/0000-0002-9845-6334Courant Institute of Mathematical Sciences, 251 Mercer Street, New York 10012-1185 NY, USA; E-mail:University of Toronto, Department of Mathematics, 40 St George Street, Toronto, ON, M5S 2E4, CanadaThis paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely only on Strichartz or virial estimates and is therefore able to treat low-power nonlinearities (hence also nonlocalised solitons) and capture the global (in space and time) behaviour of solutions.https://www.cambridge.org/core/product/identifier/S2050508622000099/type/journal_articlenonlinear Klein-Gordon equationdistorted Fourier transformscattering theorykink solutionsϕ4 theoryrelativistic Ginzburg-Landau43A3242B3735P2535Q56 |
| spellingShingle | Pierre Germain Fabio Pusateri Quadratic Klein-Gordon equations with a potential in one dimension Forum of Mathematics, Pi nonlinear Klein-Gordon equation distorted Fourier transform scattering theory kink solutions ϕ4 theory relativistic Ginzburg-Landau 43A32 42B37 35P25 35Q56 |
| title | Quadratic Klein-Gordon equations with a potential in one dimension |
| title_full | Quadratic Klein-Gordon equations with a potential in one dimension |
| title_fullStr | Quadratic Klein-Gordon equations with a potential in one dimension |
| title_full_unstemmed | Quadratic Klein-Gordon equations with a potential in one dimension |
| title_short | Quadratic Klein-Gordon equations with a potential in one dimension |
| title_sort | quadratic klein gordon equations with a potential in one dimension |
| topic | nonlinear Klein-Gordon equation distorted Fourier transform scattering theory kink solutions ϕ4 theory relativistic Ginzburg-Landau 43A32 42B37 35P25 35Q56 |
| url | https://www.cambridge.org/core/product/identifier/S2050508622000099/type/journal_article |
| work_keys_str_mv | AT pierregermain quadratickleingordonequationswithapotentialinonedimension AT fabiopusateri quadratickleingordonequationswithapotentialinonedimension |