Undular bore theory for the modified Korteweg-de Vries-Burgers equation
We consider nonlinear wave structures described by the modified Korteweg-de Vries equation with taking into account a small Burgers viscosity for the case of step-like initial conditions. The Whitham modulation equations are derived which include the small viscosity as a perturbation. It is shown th...
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| creator | de Brito, L. F. Calazans Kamchatnov, A. M |
| description | We consider nonlinear wave structures described by the modified Korteweg-de
Vries equation with taking into account a small Burgers viscosity for the case
of step-like initial conditions. The Whitham modulation equations are derived
which include the small viscosity as a perturbation. It is shown that for long
enough time of evolution this small perturbation leads to stabilization of
cnoidal bores and their main characteristics are obtained. Applicability
conditions of this approach are discussed. Analytical theory is compared with
numerical solutions and good agreement is found. |
| doi_str_mv | 10.48550/arxiv.2308.09353 |
| format | Article |
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Vries equation with taking into account a small Burgers viscosity for the case
of step-like initial conditions. The Whitham modulation equations are derived
which include the small viscosity as a perturbation. It is shown that for long
enough time of evolution this small perturbation leads to stabilization of
cnoidal bores and their main characteristics are obtained. Applicability
conditions of this approach are discussed. Analytical theory is compared with
numerical solutions and good agreement is found.</description><identifier>DOI: 10.48550/arxiv.2308.09353</identifier><language>eng</language><subject>Physics - Pattern Formation and Solitons</subject><creationdate>2023-08</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2308.09353$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2308.09353$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>de Brito, L. F. Calazans</creatorcontrib><creatorcontrib>Kamchatnov, A. M</creatorcontrib><title>Undular bore theory for the modified Korteweg-de Vries-Burgers equation</title><description>We consider nonlinear wave structures described by the modified Korteweg-de
Vries equation with taking into account a small Burgers viscosity for the case
of step-like initial conditions. The Whitham modulation equations are derived
which include the small viscosity as a perturbation. It is shown that for long
enough time of evolution this small perturbation leads to stabilization of
cnoidal bores and their main characteristics are obtained. Applicability
conditions of this approach are discussed. Analytical theory is compared with
numerical solutions and good agreement is found.</description><subject>Physics - Pattern Formation and Solitons</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz8FOAjEUBdBuXBj0A1zZH-hYaEunSyWKRhI3yHbSN-8VmgDVNzMqf6-Aq3tXN_cIcTPWla2d03eRf_JXNTG6rnQwzlyK-fseh21kCYVJ9hsqfJCp8LHKXcGcMqF8LdzTN60Vklxxpk49DLwm7iR9DrHPZX8lLlLcdnT9nyOxfHpczp7V4m3-MrtfqDj1RhmfEvjgPDgaJx_I1xNqdQghWUsAMVi0NVrAv7sB60Q-AlgDrZ0itmBG4vY8e5I0H5x3kQ_NUdScROYXpkxHvA</recordid><startdate>20230818</startdate><enddate>20230818</enddate><creator>de Brito, L. F. Calazans</creator><creator>Kamchatnov, A. M</creator><scope>ALA</scope><scope>GOX</scope></search><sort><creationdate>20230818</creationdate><title>Undular bore theory for the modified Korteweg-de Vries-Burgers equation</title><author>de Brito, L. F. Calazans ; Kamchatnov, A. M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-37ffb7957b5e1f79e782ec0999f44ebba94d48d4bd8559d8fe7abb43bc46ddcb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Physics - Pattern Formation and Solitons</topic><toplevel>online_resources</toplevel><creatorcontrib>de Brito, L. F. Calazans</creatorcontrib><creatorcontrib>Kamchatnov, A. M</creatorcontrib><collection>arXiv Nonlinear Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>de Brito, L. F. Calazans</au><au>Kamchatnov, A. M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Undular bore theory for the modified Korteweg-de Vries-Burgers equation</atitle><date>2023-08-18</date><risdate>2023</risdate><abstract>We consider nonlinear wave structures described by the modified Korteweg-de
Vries equation with taking into account a small Burgers viscosity for the case
of step-like initial conditions. The Whitham modulation equations are derived
which include the small viscosity as a perturbation. It is shown that for long
enough time of evolution this small perturbation leads to stabilization of
cnoidal bores and their main characteristics are obtained. Applicability
conditions of this approach are discussed. Analytical theory is compared with
numerical solutions and good agreement is found.</abstract><doi>10.48550/arxiv.2308.09353</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Physics - Pattern Formation and Solitons |
| title | Undular bore theory for the modified Korteweg-de Vries-Burgers equation |
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