Smooth positon solutions of the focusing modified Korteweg–de Vries equation
The n -fold Darboux transformation T n of the focusing real modified Korteweg–de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the n -soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the ei...
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| Veröffentlicht in: | Nonlinear dynamics 2017-09, Vol.89 (4), p.2299-2310 |
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| container_title | Nonlinear dynamics |
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| creator | Xing, Qiuxia Wu, Zhiwei Mihalache, Dumitru He, Jingsong |
| description | The
n
-fold Darboux transformation
T
n
of the focusing real modified Korteweg–de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the
n
-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues
λ
j
and the corresponding eigenfunctions of the associated Lax equation. The nonsingular
n
-positon solutions of the focusing mKdV equation are obtained in the special limit
λ
j
→
λ
1
, from the corresponding
n
-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the
n
-positon solution into
n
single-soliton solutions, the trajectories, and the corresponding “phase shifts” of the multi-positons are also investigated. |
| doi_str_mv | 10.1007/s11071-017-3579-x |
| format | Article |
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n
-fold Darboux transformation
T
n
of the focusing real modified Korteweg–de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the
n
-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues
λ
j
and the corresponding eigenfunctions of the associated Lax equation. The nonsingular
n
-positon solutions of the focusing mKdV equation are obtained in the special limit
λ
j
→
λ
1
, from the corresponding
n
-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the
n
-positon solution into
n
single-soliton solutions, the trajectories, and the corresponding “phase shifts” of the multi-positons are also investigated.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1007/s11071-017-3579-x</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Automotive Engineering ; Classical Mechanics ; Control ; Dynamical Systems ; Eigenvalues ; Eigenvectors ; Engineering ; Korteweg-Devries equation ; Mechanical Engineering ; Original Paper ; Representations ; Solitary waves ; Taylor series ; Vibration</subject><ispartof>Nonlinear dynamics, 2017-09, Vol.89 (4), p.2299-2310</ispartof><rights>Springer Science+Business Media Dordrecht 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><rights>Nonlinear Dynamics is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c381t-5dfb13104926a61f5b9c652545bb86079d45c892a800bc2094583d225faf57883</citedby><cites>FETCH-LOGICAL-c381t-5dfb13104926a61f5b9c652545bb86079d45c892a800bc2094583d225faf57883</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11071-017-3579-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11071-017-3579-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Xing, Qiuxia</creatorcontrib><creatorcontrib>Wu, Zhiwei</creatorcontrib><creatorcontrib>Mihalache, Dumitru</creatorcontrib><creatorcontrib>He, Jingsong</creatorcontrib><title>Smooth positon solutions of the focusing modified Korteweg–de Vries equation</title><title>Nonlinear dynamics</title><addtitle>Nonlinear Dyn</addtitle><description>The
n
-fold Darboux transformation
T
n
of the focusing real modified Korteweg–de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the
n
-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues
λ
j
and the corresponding eigenfunctions of the associated Lax equation. The nonsingular
n
-positon solutions of the focusing mKdV equation are obtained in the special limit
λ
j
→
λ
1
, from the corresponding
n
-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the
n
-positon solution into
n
single-soliton solutions, the trajectories, and the corresponding “phase shifts” of the multi-positons are also investigated.</description><subject>Automotive Engineering</subject><subject>Classical Mechanics</subject><subject>Control</subject><subject>Dynamical Systems</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Engineering</subject><subject>Korteweg-Devries equation</subject><subject>Mechanical Engineering</subject><subject>Original Paper</subject><subject>Representations</subject><subject>Solitary waves</subject><subject>Taylor series</subject><subject>Vibration</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kLtOwzAUQC0EEqXwAWyWmA3XdhzbI6p4iQoGHupm5WG3qdq4tRNRNv6BP-RLSBQGFpjucs69VwehUwrnFEBeREpBUgJUEi6kJrs9NKJCcsJSPdtHI9AsIaBhdoiOYlwCAGegRujhae19s8AbH6vG1zj6VdtUvo7YO9wsLHa-aGNVz_Hal5WrbInvfWjsm51_fXyWFr-GykZst23Wa8fowGWraE9-5hi9XF89T27J9PHmbnI5JQVXtCGidDnlFBLN0iylTuS6SAUTichzlYLUZSIKpVmmAPKCgU6E4iVjwmVOSKX4GJ0NezfBb1sbG7P0bai7k6ajdMI1cPiPoppD9wHVsqPoQBXBxxisM5tQrbPwbiiYPq4Z4pourunjml3nsMGJHVvPbfi1-U_pG1f5fLs</recordid><startdate>20170901</startdate><enddate>20170901</enddate><creator>Xing, Qiuxia</creator><creator>Wu, Zhiwei</creator><creator>Mihalache, Dumitru</creator><creator>He, Jingsong</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20170901</creationdate><title>Smooth positon solutions of the focusing modified Korteweg–de Vries equation</title><author>Xing, Qiuxia ; Wu, Zhiwei ; Mihalache, Dumitru ; He, Jingsong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-5dfb13104926a61f5b9c652545bb86079d45c892a800bc2094583d225faf57883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Automotive Engineering</topic><topic>Classical Mechanics</topic><topic>Control</topic><topic>Dynamical Systems</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Engineering</topic><topic>Korteweg-Devries equation</topic><topic>Mechanical Engineering</topic><topic>Original Paper</topic><topic>Representations</topic><topic>Solitary waves</topic><topic>Taylor series</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xing, Qiuxia</creatorcontrib><creatorcontrib>Wu, Zhiwei</creatorcontrib><creatorcontrib>Mihalache, Dumitru</creatorcontrib><creatorcontrib>He, Jingsong</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Nonlinear dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xing, Qiuxia</au><au>Wu, Zhiwei</au><au>Mihalache, Dumitru</au><au>He, Jingsong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Smooth positon solutions of the focusing modified Korteweg–de Vries equation</atitle><jtitle>Nonlinear dynamics</jtitle><stitle>Nonlinear Dyn</stitle><date>2017-09-01</date><risdate>2017</risdate><volume>89</volume><issue>4</issue><spage>2299</spage><epage>2310</epage><pages>2299-2310</pages><issn>0924-090X</issn><eissn>1573-269X</eissn><abstract>The
n
-fold Darboux transformation
T
n
of the focusing real modified Korteweg–de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the
n
-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues
λ
j
and the corresponding eigenfunctions of the associated Lax equation. The nonsingular
n
-positon solutions of the focusing mKdV equation are obtained in the special limit
λ
j
→
λ
1
, from the corresponding
n
-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the
n
-positon solution into
n
single-soliton solutions, the trajectories, and the corresponding “phase shifts” of the multi-positons are also investigated.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11071-017-3579-x</doi><tpages>12</tpages></addata></record> |
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| ispartof | Nonlinear dynamics, 2017-09, Vol.89 (4), p.2299-2310 |
| issn | 0924-090X 1573-269X |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Automotive Engineering Classical Mechanics Control Dynamical Systems Eigenvalues Eigenvectors Engineering Korteweg-Devries equation Mechanical Engineering Original Paper Representations Solitary waves Taylor series Vibration |
| title | Smooth positon solutions of the focusing modified Korteweg–de Vries equation |
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