Lie symmetry analysis for similarity reduction and exact solutions of modified KdV–Zakharov–Kuznetsov equation
In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the ( 3 + 1 ) -dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new part...
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| Veröffentlicht in: | Nonlinear dynamics 2017-02, Vol.87 (3), p.1995-2000 |
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| container_end_page | 2000 |
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| container_issue | 3 |
| container_start_page | 1995 |
| container_title | Nonlinear dynamics |
| container_volume | 87 |
| creator | Sahoo, S. Garai, G. Saha Ray, S. |
| description | In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the
(
3
+
1
)
-dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new partial differential equation with less number of independent variables, and again using Lie group symmetry method, the new partial differential equation is reduced into an ordinary differential equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV–ZK equation. In addition to that, solitary wave solutions of the mKdV–ZK equation are derived from the reduction equation. Thus, we obtain some new exact explicit solutions of the
(
3
+
1
)
-dimensional mKdV–ZK equation which describes the dynamics of nonlinear waves in plasmas. |
| doi_str_mv | 10.1007/s11071-016-3169-3 |
| format | Article |
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(
3
+
1
)
-dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new partial differential equation with less number of independent variables, and again using Lie group symmetry method, the new partial differential equation is reduced into an ordinary differential equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV–ZK equation. In addition to that, solitary wave solutions of the mKdV–ZK equation are derived from the reduction equation. Thus, we obtain some new exact explicit solutions of the
(
3
+
1
)
-dimensional mKdV–ZK equation which describes the dynamics of nonlinear waves in plasmas.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1007/s11071-016-3169-3</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Automotive Engineering ; Classical Mechanics ; Commutators ; Control ; Dynamical Systems ; Engineering ; Exact solutions ; Group theory ; Independent variables ; Korteweg-Devries equation ; Lie groups ; Mathematical analysis ; Mechanical Engineering ; Nonlinear dynamics ; Original Paper ; Partial differential equations ; Plasmas (physics) ; Reduction ; Similarity ; Similarity solutions ; Solitary waves ; Symmetry ; Vibration</subject><ispartof>Nonlinear dynamics, 2017-02, Vol.87 (3), p.1995-2000</ispartof><rights>Springer Science+Business Media Dordrecht 2016</rights><rights>Copyright Springer Science & Business Media 2017</rights><rights>Nonlinear Dynamics is a copyright of Springer, (2016). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c447t-8edcd395a40aee8506606acad1fbaec8434527dd304b99fb5e4a86deec8432723</citedby><cites>FETCH-LOGICAL-c447t-8edcd395a40aee8506606acad1fbaec8434527dd304b99fb5e4a86deec8432723</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/s11071-016-3169-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11071-016-3169-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27915,27916,41479,42548,51310</link.rule.ids></links><search><creatorcontrib>Sahoo, S.</creatorcontrib><creatorcontrib>Garai, G.</creatorcontrib><creatorcontrib>Saha Ray, S.</creatorcontrib><title>Lie symmetry analysis for similarity reduction and exact solutions of modified KdV–Zakharov–Kuznetsov equation</title><title>Nonlinear dynamics</title><addtitle>Nonlinear Dyn</addtitle><description>In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the
(
3
+
1
)
-dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new partial differential equation with less number of independent variables, and again using Lie group symmetry method, the new partial differential equation is reduced into an ordinary differential equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV–ZK equation. In addition to that, solitary wave solutions of the mKdV–ZK equation are derived from the reduction equation. Thus, we obtain some new exact explicit solutions of the
(
3
+
1
)
-dimensional mKdV–ZK equation which describes the dynamics of nonlinear waves in plasmas.</description><subject>Automotive Engineering</subject><subject>Classical Mechanics</subject><subject>Commutators</subject><subject>Control</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Exact solutions</subject><subject>Group theory</subject><subject>Independent variables</subject><subject>Korteweg-Devries equation</subject><subject>Lie groups</subject><subject>Mathematical analysis</subject><subject>Mechanical Engineering</subject><subject>Nonlinear dynamics</subject><subject>Original Paper</subject><subject>Partial differential equations</subject><subject>Plasmas (physics)</subject><subject>Reduction</subject><subject>Similarity</subject><subject>Similarity solutions</subject><subject>Solitary waves</subject><subject>Symmetry</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>eNp9kctu1TAQhi0EEofSB2BniQ2b0PElFy-ript6pG4AVd1YPvEEXJK49SRV0xXv0Dfsk-BwWFRIsBpr_P3_Yj7GXgl4KwDqIxICalGAqAolKlOoJ2wjyloVsjLnT9kGjNQFGDh_zl4QXQKAktBsWNoG5LQMA05p4W50_UKBeBcTpzCE3qUwLTyhn9spxDETnuOtaydOsZ_XFfHY8SH60AX0_NR_ffh5f-F-fHcp3uTn6Xw34kTxhuP17NbAS_ascz3h4Z95wL68f_f55GOxPfvw6eR4W7Ra11PRoG-9MqXT4BCbEqoKKtc6L7qdw7bRSpey9l6B3hnT7UrUrqk8_v6StVQH7M2-9yrF6xlpskOgFvvejRhnsqIxyggttM7o67_QyzinfAyyUpYm9zVQ_48STQaMAbNSYk-1KRIl7OxVCoNLixVgV1d278pmV3Z1ZVXOyH2GMjt-w_So-Z-hX7glmpg</recordid><startdate>20170201</startdate><enddate>20170201</enddate><creator>Sahoo, S.</creator><creator>Garai, G.</creator><creator>Saha Ray, S.</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><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20170201</creationdate><title>Lie symmetry analysis for similarity reduction and exact solutions of modified KdV–Zakharov–Kuznetsov equation</title><author>Sahoo, S. ; Garai, G. ; Saha Ray, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c447t-8edcd395a40aee8506606acad1fbaec8434527dd304b99fb5e4a86deec8432723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Automotive Engineering</topic><topic>Classical Mechanics</topic><topic>Commutators</topic><topic>Control</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Exact solutions</topic><topic>Group theory</topic><topic>Independent variables</topic><topic>Korteweg-Devries equation</topic><topic>Lie groups</topic><topic>Mathematical analysis</topic><topic>Mechanical Engineering</topic><topic>Nonlinear dynamics</topic><topic>Original Paper</topic><topic>Partial differential equations</topic><topic>Plasmas (physics)</topic><topic>Reduction</topic><topic>Similarity</topic><topic>Similarity solutions</topic><topic>Solitary waves</topic><topic>Symmetry</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sahoo, S.</creatorcontrib><creatorcontrib>Garai, G.</creatorcontrib><creatorcontrib>Saha Ray, S.</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 (ProQuest)</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><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sahoo, S.</au><au>Garai, G.</au><au>Saha Ray, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lie symmetry analysis for similarity reduction and exact solutions of modified KdV–Zakharov–Kuznetsov equation</atitle><jtitle>Nonlinear dynamics</jtitle><stitle>Nonlinear Dyn</stitle><date>2017-02-01</date><risdate>2017</risdate><volume>87</volume><issue>3</issue><spage>1995</spage><epage>2000</epage><pages>1995-2000</pages><issn>0924-090X</issn><eissn>1573-269X</eissn><abstract>In this paper, the Lie group analysis is used to carry out the similarity reduction and exact solutions of the
(
3
+
1
)
-dimensional modified KdV–Zakharov–Kuznetsov equation. This research deals with the similarity solutions of mKdV–ZK equation. The mKdV–ZK equation has been reduced into a new partial differential equation with less number of independent variables, and again using Lie group symmetry method, the new partial differential equation is reduced into an ordinary differential equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV–ZK equation. In addition to that, solitary wave solutions of the mKdV–ZK equation are derived from the reduction equation. Thus, we obtain some new exact explicit solutions of the
(
3
+
1
)
-dimensional mKdV–ZK equation which describes the dynamics of nonlinear waves in plasmas.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11071-016-3169-3</doi><tpages>6</tpages></addata></record> |
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| ispartof | Nonlinear dynamics, 2017-02, Vol.87 (3), p.1995-2000 |
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| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Automotive Engineering Classical Mechanics Commutators Control Dynamical Systems Engineering Exact solutions Group theory Independent variables Korteweg-Devries equation Lie groups Mathematical analysis Mechanical Engineering Nonlinear dynamics Original Paper Partial differential equations Plasmas (physics) Reduction Similarity Similarity solutions Solitary waves Symmetry Vibration |
| title | Lie symmetry analysis for similarity reduction and exact solutions of modified KdV–Zakharov–Kuznetsov equation |
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