Decay of solitary waves of fractional Korteweg-de Vries type equations
We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the 1-dimensional semi-linear fractional equations:|D|αu+u−f(u)=0, with α∈(0,2), a prescribed coefficient p⁎(α), and a non-linearity f(u)=|u|p−1u for p∈(1,p⁎(α)), or f(u)=up with an integer p∈[2;p⁎(α)). A...
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| Veröffentlicht in: | Journal of Differential Equations 2023-08, Vol.363, p.243-274 |
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| container_title | Journal of Differential Equations |
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| creator | Eychenne, Arnaud Valet, Frédéric |
| description | We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the 1-dimensional semi-linear fractional equations:|D|αu+u−f(u)=0, with α∈(0,2), a prescribed coefficient p⁎(α), and a non-linearity f(u)=|u|p−1u for p∈(1,p⁎(α)), or f(u)=up with an integer p∈[2;p⁎(α)). Asymptotic developments of order 1 at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion α and of the non-linearity p. The main tools are the kernel formulation introduced by Bona and Li, and an accurate description of the kernel by complex analysis theory. |
| doi_str_mv | 10.1016/j.jde.2023.03.012 |
| format | Article |
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Asymptotic developments of order 1 at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion α and of the non-linearity p. 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Asymptotic developments of order 1 at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion α and of the non-linearity p. The main tools are the kernel formulation introduced by Bona and Li, and an accurate description of the kernel by complex analysis theory.</description><subject>Asymptotic expansion</subject><subject>Fractional KdV equation</subject><subject>Mathematics</subject><subject>Soliton solutions</subject><issn>0022-0396</issn><issn>1090-2732</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UMFOwzAMjRBIjMEHcOuVQ4udNGsrThMwhpjEBbhGWeJAqrGOpGza35NqiCPSk2zZ71l-j7FLhAIBJ9dt0VoqOHBRQALyIzZCaCDnleDHbATAeQ6imZyysxhbAEQ5kSM2uyOj91nnstitfK_DPtvpLcVh4oI2ve_WepU9daGnHb3nlrK34NO-328oo69vPTDiOTtxehXp4reO2evs_uV2ni-eHx5vp4vciKrs82rZVM5JIGmsXFbCVqbmjZRcpraG9L4lwGrpsBalxcaVTVMarGUtrSvBiDG7Otz90Cu1Cf4zPaw67dV8ulDDDEqRDCNsMXHxwDWhizGQ-xMgqCE01aoUmhpCU5CAPGluDhpKJraegorG09qQ9YFMr2zn_1H_ANW0cxg</recordid><startdate>20230805</startdate><enddate>20230805</enddate><creator>Eychenne, Arnaud</creator><creator>Valet, Frédéric</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5479-2352</orcidid></search><sort><creationdate>20230805</creationdate><title>Decay of solitary waves of fractional Korteweg-de Vries type equations</title><author>Eychenne, Arnaud ; Valet, Frédéric</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c374t-7b97ff50e5cd5b73d7c82955253d780202de017bf1834d19f4994c18585df40c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Asymptotic expansion</topic><topic>Fractional KdV equation</topic><topic>Mathematics</topic><topic>Soliton solutions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Eychenne, Arnaud</creatorcontrib><creatorcontrib>Valet, Frédéric</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of Differential Equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Eychenne, Arnaud</au><au>Valet, Frédéric</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Decay of solitary waves of fractional Korteweg-de Vries type equations</atitle><jtitle>Journal of Differential Equations</jtitle><date>2023-08-05</date><risdate>2023</risdate><volume>363</volume><spage>243</spage><epage>274</epage><pages>243-274</pages><issn>0022-0396</issn><eissn>1090-2732</eissn><abstract>We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the 1-dimensional semi-linear fractional equations:|D|αu+u−f(u)=0, with α∈(0,2), a prescribed coefficient p⁎(α), and a non-linearity f(u)=|u|p−1u for p∈(1,p⁎(α)), or f(u)=up with an integer p∈[2;p⁎(α)). Asymptotic developments of order 1 at infinity of solutions are given, as well as second order developments for positive solutions, in terms of the coefficient of dispersion α and of the non-linearity p. The main tools are the kernel formulation introduced by Bona and Li, and an accurate description of the kernel by complex analysis theory.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.jde.2023.03.012</doi><tpages>32</tpages><orcidid>https://orcid.org/0000-0002-5479-2352</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of Differential Equations, 2023-08, Vol.363, p.243-274 |
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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Asymptotic expansion Fractional KdV equation Mathematics Soliton solutions |
| title | Decay of solitary waves of fractional Korteweg-de Vries type equations |
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