Asymptotic stability of solitary waves in generalized Gross--Neveu model
For the nonlinear Dirac equation in (1+1)D with scalar self-interaction (Gross--Neveu model), with quintic and higher order nonlinearities (and within certain range of the parameters), we prove that solitary wave solutions are asymptotically stable in the "even" subspace of perturbations (...
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| creator | Comech, Andrew Van Phan, Tuoc Stefanov, Atanas |
| description | For the nonlinear Dirac equation in (1+1)D with scalar self-interaction
(Gross--Neveu model), with quintic and higher order nonlinearities (and within
certain range of the parameters), we prove that solitary wave solutions are
asymptotically stable in the "even" subspace of perturbations (to ignore
translations and eigenvalues $\pm 2\omega i$). The asymptotic stability is
proved for initial data in $H^1$. The approach is based on the spectral
information about the linearization at solitary waves which we justify by
numerical simulations. For the proof, we develop the spectral theory for the
linearized operators and obtain appropriate estimates in mixed Lebesgue spaces,
with and without weights. |
| doi_str_mv | 10.48550/arxiv.1407.0606 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1407_0606</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1407_0606</sourcerecordid><originalsourceid>FETCH-LOGICAL-a656-adb54044c9f9687cba2fc02505904f668190bfc4c70fdf785478426eb024001d3</originalsourceid><addsrcrecordid>eNotzztPwzAUBWAvDKiwMyH_AYeb9PqRsaqgrVTRpXvkJ7KU1JUdAuHXtwWmc6aj8xHyVEOFinN40fk7TlWNICsQIO7JdlXm4TymMVpaRm1iH8eZpkBLujadZ_qlJ19oPNEPf_JZ9_HHO7rJqRTG3v3kP-mQnO8fyF3QffGP_7kgx7fX43rL9ofNbr3aMy24YNoZjoBo29AKJa3RTbDQcOAtYBBC1S2YYNFKCC5IxVEqbIQ30CBA7ZYL8vw3-yvpzjkO15PdTdTdRMsLcp1GIA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Asymptotic stability of solitary waves in generalized Gross--Neveu model</title><source>arXiv.org</source><creator>Comech, Andrew ; Van Phan, Tuoc ; Stefanov, Atanas</creator><creatorcontrib>Comech, Andrew ; Van Phan, Tuoc ; Stefanov, Atanas</creatorcontrib><description>For the nonlinear Dirac equation in (1+1)D with scalar self-interaction
(Gross--Neveu model), with quintic and higher order nonlinearities (and within
certain range of the parameters), we prove that solitary wave solutions are
asymptotically stable in the "even" subspace of perturbations (to ignore
translations and eigenvalues $\pm 2\omega i$). The asymptotic stability is
proved for initial data in $H^1$. The approach is based on the spectral
information about the linearization at solitary waves which we justify by
numerical simulations. For the proof, we develop the spectral theory for the
linearized operators and obtain appropriate estimates in mixed Lebesgue spaces,
with and without weights.</description><identifier>DOI: 10.48550/arxiv.1407.0606</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2014-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1407.0606$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1407.0606$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Comech, Andrew</creatorcontrib><creatorcontrib>Van Phan, Tuoc</creatorcontrib><creatorcontrib>Stefanov, Atanas</creatorcontrib><title>Asymptotic stability of solitary waves in generalized Gross--Neveu model</title><description>For the nonlinear Dirac equation in (1+1)D with scalar self-interaction
(Gross--Neveu model), with quintic and higher order nonlinearities (and within
certain range of the parameters), we prove that solitary wave solutions are
asymptotically stable in the "even" subspace of perturbations (to ignore
translations and eigenvalues $\pm 2\omega i$). The asymptotic stability is
proved for initial data in $H^1$. The approach is based on the spectral
information about the linearization at solitary waves which we justify by
numerical simulations. For the proof, we develop the spectral theory for the
linearized operators and obtain appropriate estimates in mixed Lebesgue spaces,
with and without weights.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzztPwzAUBWAvDKiwMyH_AYeb9PqRsaqgrVTRpXvkJ7KU1JUdAuHXtwWmc6aj8xHyVEOFinN40fk7TlWNICsQIO7JdlXm4TymMVpaRm1iH8eZpkBLujadZ_qlJ19oPNEPf_JZ9_HHO7rJqRTG3v3kP-mQnO8fyF3QffGP_7kgx7fX43rL9ofNbr3aMy24YNoZjoBo29AKJa3RTbDQcOAtYBBC1S2YYNFKCC5IxVEqbIQ30CBA7ZYL8vw3-yvpzjkO15PdTdTdRMsLcp1GIA</recordid><startdate>20140702</startdate><enddate>20140702</enddate><creator>Comech, Andrew</creator><creator>Van Phan, Tuoc</creator><creator>Stefanov, Atanas</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20140702</creationdate><title>Asymptotic stability of solitary waves in generalized Gross--Neveu model</title><author>Comech, Andrew ; Van Phan, Tuoc ; Stefanov, Atanas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a656-adb54044c9f9687cba2fc02505904f668190bfc4c70fdf785478426eb024001d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Comech, Andrew</creatorcontrib><creatorcontrib>Van Phan, Tuoc</creatorcontrib><creatorcontrib>Stefanov, Atanas</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Comech, Andrew</au><au>Van Phan, Tuoc</au><au>Stefanov, Atanas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic stability of solitary waves in generalized Gross--Neveu model</atitle><date>2014-07-02</date><risdate>2014</risdate><abstract>For the nonlinear Dirac equation in (1+1)D with scalar self-interaction
(Gross--Neveu model), with quintic and higher order nonlinearities (and within
certain range of the parameters), we prove that solitary wave solutions are
asymptotically stable in the "even" subspace of perturbations (to ignore
translations and eigenvalues $\pm 2\omega i$). The asymptotic stability is
proved for initial data in $H^1$. The approach is based on the spectral
information about the linearization at solitary waves which we justify by
numerical simulations. For the proof, we develop the spectral theory for the
linearized operators and obtain appropriate estimates in mixed Lebesgue spaces,
with and without weights.</abstract><doi>10.48550/arxiv.1407.0606</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Asymptotic stability of solitary waves in generalized Gross--Neveu model |
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