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Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph
We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, δ , or δ ′ boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is b...
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Published in: | Journal of evolution equations 2021-03, Vol.21 (1), p.297-312 |
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container_title | Journal of evolution equations |
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creator | Aoki, Kazuki Inui, Takahisa Mizutani, Haruya |
description | We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet,
δ
, or
δ
′
boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi (Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations), who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions. |
doi_str_mv | 10.1007/s00028-020-00579-w |
format | article |
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δ
, or
δ
′
boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi (Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations), who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.</description><identifier>ISSN: 1424-3199</identifier><identifier>EISSN: 1424-3202</identifier><identifier>DOI: 10.1007/s00028-020-00579-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Boundary conditions ; Dirichlet problem ; Euclidean geometry ; Euclidean space ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Scattering ; Schrodinger equation ; Solitary waves ; Standing waves</subject><ispartof>Journal of evolution equations, 2021-03, Vol.21 (1), p.297-312</ispartof><rights>Springer Nature Switzerland AG 2020</rights><rights>Springer Nature Switzerland AG 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-dce8577cfd1e12fca9193a24805d08b798bd1981da43c8988b206566988e7d613</citedby><cites>FETCH-LOGICAL-c319t-dce8577cfd1e12fca9193a24805d08b798bd1981da43c8988b206566988e7d613</cites><orcidid>0000-0001-9951-3890</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,786,790,27957,27958</link.rule.ids></links><search><creatorcontrib>Aoki, Kazuki</creatorcontrib><creatorcontrib>Inui, Takahisa</creatorcontrib><creatorcontrib>Mizutani, Haruya</creatorcontrib><title>Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph</title><title>Journal of evolution equations</title><addtitle>J. Evol. Equ</addtitle><description>We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet,
δ
, or
δ
′
boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi (Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations), who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.</description><subject>Analysis</subject><subject>Boundary conditions</subject><subject>Dirichlet problem</subject><subject>Euclidean geometry</subject><subject>Euclidean space</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Scattering</subject><subject>Schrodinger equation</subject><subject>Solitary waves</subject><subject>Standing waves</subject><issn>1424-3199</issn><issn>1424-3202</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhS0EEqVwAVaWWAfGzo_tJaooIFViAawt13HaVMFObZeoF-MCXAyXgNixmqeZeW9GH0KXBK4JALsJAEB5BhQygJKJbDhCE1LQIssp0ONfTYQ4RWchbAAIK3k5QXau2m7nDXYNDlrFaHxrVzg6HKKy9UEP6t0E3DiPFX7Wa__5cWgbj812p2LrLB7auMads6vMqzTB1tmutUb5Nu5xmqcoj1de9etzdNKoLpiLnzpFr_O7l9lDtni6f5zdLjKdfoxZrQ0vGdNNTQyhjVaCiFzRgkNZA18ywZc1EZzUqsg1F5wvKVRlVSVlWF2RfIquxtzeu-3OhCg3budtOilpCYyBgEKkLTpuae9C8KaRvW_flN9LAvLAVY5cZeIqv7nKIZny0RR6_83hL_of1xfrMn1d</recordid><startdate>20210301</startdate><enddate>20210301</enddate><creator>Aoki, Kazuki</creator><creator>Inui, Takahisa</creator><creator>Mizutani, Haruya</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9951-3890</orcidid></search><sort><creationdate>20210301</creationdate><title>Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph</title><author>Aoki, Kazuki ; Inui, Takahisa ; Mizutani, Haruya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-dce8577cfd1e12fca9193a24805d08b798bd1981da43c8988b206566988e7d613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Analysis</topic><topic>Boundary conditions</topic><topic>Dirichlet problem</topic><topic>Euclidean geometry</topic><topic>Euclidean space</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Scattering</topic><topic>Schrodinger equation</topic><topic>Solitary waves</topic><topic>Standing waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aoki, Kazuki</creatorcontrib><creatorcontrib>Inui, Takahisa</creatorcontrib><creatorcontrib>Mizutani, Haruya</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of evolution equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aoki, Kazuki</au><au>Inui, Takahisa</au><au>Mizutani, Haruya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph</atitle><jtitle>Journal of evolution equations</jtitle><stitle>J. Evol. Equ</stitle><date>2021-03-01</date><risdate>2021</risdate><volume>21</volume><issue>1</issue><spage>297</spage><epage>312</epage><pages>297-312</pages><issn>1424-3199</issn><eissn>1424-3202</eissn><abstract>We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet,
δ
, or
δ
′
boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi (Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations), who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00028-020-00579-w</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0001-9951-3890</orcidid></addata></record> |
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subjects | Analysis Boundary conditions Dirichlet problem Euclidean geometry Euclidean space Mathematics Mathematics and Statistics Nonlinearity Scattering Schrodinger equation Solitary waves Standing waves |
title | Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph |
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