Long-Time approximations of small-amplitude, long-wavelength FPUT solutions
It is well known that the Korteweg-de Vries (KdV) equation and its generalizations serve as modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation estimates and other such results have been proved in this case. However, situation...
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| creator | Norton, Trevor Wayne, C. Eugene |
| description | It is well known that the Korteweg-de Vries (KdV) equation and its
generalizations serve as modulation equations for traveling wave solutions to
generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation
estimates and other such results have been proved in this case. However,
situations in which the defocusing modified KdV (mKdV) equation is expected to
be the modulation equation have been much less studied. As seen in numerical
experiments, the kink solution of the mKdV seems essential in understanding the
$\beta$-FPUT recurrence. In this paper, we derive explicit approximation
results for solutions of the FPUT using the mKdV as a modulation equation. In
contrast to previous work, our estimates allow for solutions to be
non-localized as to allow approximate kink solutions. These results allow us to
conclude meta-stability results of kink-like solutions of the FPUT. |
| doi_str_mv | 10.48550/arxiv.2306.14999 |
| format | Article |
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generalizations serve as modulation equations for traveling wave solutions to
generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation
estimates and other such results have been proved in this case. However,
situations in which the defocusing modified KdV (mKdV) equation is expected to
be the modulation equation have been much less studied. As seen in numerical
experiments, the kink solution of the mKdV seems essential in understanding the
$\beta$-FPUT recurrence. In this paper, we derive explicit approximation
results for solutions of the FPUT using the mKdV as a modulation equation. In
contrast to previous work, our estimates allow for solutions to be
non-localized as to allow approximate kink solutions. These results allow us to
conclude meta-stability results of kink-like solutions of the FPUT.</description><identifier>DOI: 10.48550/arxiv.2306.14999</identifier><language>eng</language><subject>Mathematics - Dynamical Systems</subject><creationdate>2023-06</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2306.14999$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2306.14999$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Norton, Trevor</creatorcontrib><creatorcontrib>Wayne, C. Eugene</creatorcontrib><title>Long-Time approximations of small-amplitude, long-wavelength FPUT solutions</title><description>It is well known that the Korteweg-de Vries (KdV) equation and its
generalizations serve as modulation equations for traveling wave solutions to
generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation
estimates and other such results have been proved in this case. However,
situations in which the defocusing modified KdV (mKdV) equation is expected to
be the modulation equation have been much less studied. As seen in numerical
experiments, the kink solution of the mKdV seems essential in understanding the
$\beta$-FPUT recurrence. In this paper, we derive explicit approximation
results for solutions of the FPUT using the mKdV as a modulation equation. In
contrast to previous work, our estimates allow for solutions to be
non-localized as to allow approximate kink solutions. These results allow us to
conclude meta-stability results of kink-like solutions of the FPUT.</description><subject>Mathematics - Dynamical Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7FOwzAURb0woMIHMOEPwMEvtl_sEVUUEJFgCHPkxE6x5MRRkpby99DAdJd7j-4h5AZ4JrVS_N5Op3DMcsExA2mMuSSvZRr2rAq9p3Ycp3QKvV1CGmaaOjr3NkZm-zGG5eD8HY3n8pc9-uiH_fJJd-8fFZ1TPKyTK3LR2Tj76__ckGr3WG2fWfn29LJ9KJnFwjAQrnECMNfacUStvQGJrTI5Kt9C69E2nS0kSgCucw3YaN2qwgGXUvlCbMjtH3a1qcfp9_L0XZ-t6tVK_ACtUEcz</recordid><startdate>20230626</startdate><enddate>20230626</enddate><creator>Norton, Trevor</creator><creator>Wayne, C. Eugene</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230626</creationdate><title>Long-Time approximations of small-amplitude, long-wavelength FPUT solutions</title><author>Norton, Trevor ; Wayne, C. Eugene</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-13dbd316288d06688e9146c59265ec1ce6abfa746411082816b88c57d10445e73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Dynamical Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Norton, Trevor</creatorcontrib><creatorcontrib>Wayne, C. Eugene</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Norton, Trevor</au><au>Wayne, C. Eugene</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Long-Time approximations of small-amplitude, long-wavelength FPUT solutions</atitle><date>2023-06-26</date><risdate>2023</risdate><abstract>It is well known that the Korteweg-de Vries (KdV) equation and its
generalizations serve as modulation equations for traveling wave solutions to
generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation
estimates and other such results have been proved in this case. However,
situations in which the defocusing modified KdV (mKdV) equation is expected to
be the modulation equation have been much less studied. As seen in numerical
experiments, the kink solution of the mKdV seems essential in understanding the
$\beta$-FPUT recurrence. In this paper, we derive explicit approximation
results for solutions of the FPUT using the mKdV as a modulation equation. In
contrast to previous work, our estimates allow for solutions to be
non-localized as to allow approximate kink solutions. These results allow us to
conclude meta-stability results of kink-like solutions of the FPUT.</abstract><doi>10.48550/arxiv.2306.14999</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems |
| title | Long-Time approximations of small-amplitude, long-wavelength FPUT solutions |
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