Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method
We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2 versions of KP equations with integrable boundary condition $u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov and derived general determinant formula for such solutions. We demo...
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| creator | Dubrovsky, V. G Topovsky, A. V |
| description | We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2
versions of KP equations with integrable boundary condition
$u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of
Zakharov and Manakov and derived general determinant formula for such
solutions. We demonstrated how reality and boundary conditions for the field
$u$ in the framework of $\overline\partial$-dressing method can be exactly
satisfied. Here we present explicit examples of two-lump solutions with
integrable boundary as nonlinear superpositions of two more simpler "deformed"
one-lump solutions: the fulfillment of boundary condition leads to formation of
certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of
standing waves on string with fixed end points. |
| doi_str_mv | 10.48550/arxiv.2003.01716 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2003_01716</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2003_01716</sourcerecordid><originalsourceid>FETCH-arxiv_primary_2003_017163</originalsourceid><addsrcrecordid>eNqFzr0KwkAQBOBrLER9ACu3SJt4MUbtRRFEsLAUwoVskoXLXbyfqG-vCfZWw8AwfIzNYx6td2nKl8K8qItWnCcRj7fxZsyKi5eOQumbFqyW3pFWFnQJ5yvgw4u-w5NcDaQcVkbkEiHXXhXCvKEjAcFdd2gkKby3wjgSMggLg9aSqqBBV-tiykalkBZnv5ywxfFw25_CwZO1hprvW9a7ssGV_F98AOtERKs</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method</title><source>arXiv.org</source><creator>Dubrovsky, V. G ; Topovsky, A. V</creator><creatorcontrib>Dubrovsky, V. G ; Topovsky, A. V</creatorcontrib><description>We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2
versions of KP equations with integrable boundary condition
$u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of
Zakharov and Manakov and derived general determinant formula for such
solutions. We demonstrated how reality and boundary conditions for the field
$u$ in the framework of $\overline\partial$-dressing method can be exactly
satisfied. Here we present explicit examples of two-lump solutions with
integrable boundary as nonlinear superpositions of two more simpler "deformed"
one-lump solutions: the fulfillment of boundary condition leads to formation of
certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of
standing waves on string with fixed end points.</description><identifier>DOI: 10.48550/arxiv.2003.01716</identifier><language>eng</language><subject>Physics - Exactly Solvable and Integrable Systems</subject><creationdate>2020-03</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2003.01716$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.1016/j.physd.2021.133025$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2003.01716$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dubrovsky, V. G</creatorcontrib><creatorcontrib>Topovsky, A. V</creatorcontrib><title>Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method</title><description>We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2
versions of KP equations with integrable boundary condition
$u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of
Zakharov and Manakov and derived general determinant formula for such
solutions. We demonstrated how reality and boundary conditions for the field
$u$ in the framework of $\overline\partial$-dressing method can be exactly
satisfied. Here we present explicit examples of two-lump solutions with
integrable boundary as nonlinear superpositions of two more simpler "deformed"
one-lump solutions: the fulfillment of boundary condition leads to formation of
certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of
standing waves on string with fixed end points.</description><subject>Physics - Exactly Solvable and Integrable Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFzr0KwkAQBOBrLER9ACu3SJt4MUbtRRFEsLAUwoVskoXLXbyfqG-vCfZWw8AwfIzNYx6td2nKl8K8qItWnCcRj7fxZsyKi5eOQumbFqyW3pFWFnQJ5yvgw4u-w5NcDaQcVkbkEiHXXhXCvKEjAcFdd2gkKby3wjgSMggLg9aSqqBBV-tiykalkBZnv5ywxfFw25_CwZO1hprvW9a7ssGV_F98AOtERKs</recordid><startdate>20200303</startdate><enddate>20200303</enddate><creator>Dubrovsky, V. G</creator><creator>Topovsky, A. V</creator><scope>ALA</scope><scope>GOX</scope></search><sort><creationdate>20200303</creationdate><title>Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method</title><author>Dubrovsky, V. G ; Topovsky, A. V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2003_017163</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Physics - Exactly Solvable and Integrable Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Dubrovsky, V. G</creatorcontrib><creatorcontrib>Topovsky, A. V</creatorcontrib><collection>arXiv Nonlinear Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dubrovsky, V. G</au><au>Topovsky, A. V</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method</atitle><date>2020-03-03</date><risdate>2020</risdate><abstract>We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2
versions of KP equations with integrable boundary condition
$u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of
Zakharov and Manakov and derived general determinant formula for such
solutions. We demonstrated how reality and boundary conditions for the field
$u$ in the framework of $\overline\partial$-dressing method can be exactly
satisfied. Here we present explicit examples of two-lump solutions with
integrable boundary as nonlinear superpositions of two more simpler "deformed"
one-lump solutions: the fulfillment of boundary condition leads to formation of
certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of
standing waves on string with fixed end points.</abstract><doi>10.48550/arxiv.2003.01716</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Physics - Exactly Solvable and Integrable Systems |
| title | Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method |
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