Loading…
A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions
In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the gov...
Saved in:
Published in: | Nonlinear dynamics 2022-02, Vol.107 (3), p.2689-2701 |
---|---|
Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
cited_by | cdi_FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603 |
---|---|
cites | cdi_FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603 |
container_end_page | 2701 |
container_issue | 3 |
container_start_page | 2689 |
container_title | Nonlinear dynamics |
container_volume | 107 |
creator | Malik, Sandeep Kumar, Sachin Das, Amiya |
description | In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the governing equation has been reduced to ordinary differential equations. Further, we have constructed the dark, bright, singular and combo bright-singular soliton solutions via different techniques. The hyperbolic function method, the Kudryashov method and a new version of Kudryashov method are among these techniques. Moreover, by using phase plane theory, we investigate the stability of the corresponding dynamical system. |
doi_str_mv | 10.1007/s11071-021-07075-x |
format | article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2628404630</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2628404630</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603</originalsourceid><addsrcrecordid>eNp9kM9KAzEQxoMoWKsv4CngRdHoJLvZJN5K8R8WvKj0FrKbtKR0d9vNLrQ338E39EnMWsGbh-EbZr7fkHwInVK4pgDiJlAKghJgsQQITjZ7aEC5SAjL1HQfDUCxlICC6SE6CmEBAAkDOUB-hM_ZJb0g1peuCr6uzBIXdZn7yln8bN-_Pj7LKNitO9PG9S32Vevmjcn90rfbKxza3xabyG6DD7GxONRxVle9dj0XjtHBzCyDO_nVIXq7v3sdP5LJy8PTeDQhRUJVS6RQuXEunaUyEcpkhQTGlGScW2koh_ifOGBGcqOUlalVnOeW5jYVtMgySIbobHd31dTrzoVWL-quiU8LmmVMppBmSe9iO1fR1CE0bqZXjS9Ns9UUdB-p3kWqY6T6J1K9iVCyg0I0V3PX_J3-h_oGx-J6YA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2628404630</pqid></control><display><type>article</type><title>A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions</title><source>Springer Link</source><creator>Malik, Sandeep ; Kumar, Sachin ; Das, Amiya</creator><creatorcontrib>Malik, Sandeep ; Kumar, Sachin ; Das, Amiya</creatorcontrib><description>In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the governing equation has been reduced to ordinary differential equations. Further, we have constructed the dark, bright, singular and combo bright-singular soliton solutions via different techniques. The hyperbolic function method, the Kudryashov method and a new version of Kudryashov method are among these techniques. Moreover, by using phase plane theory, we investigate the stability of the corresponding dynamical system.</description><identifier>ISSN: 0924-090X</identifier><identifier>EISSN: 1573-269X</identifier><identifier>DOI: 10.1007/s11071-021-07075-x</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Automotive Engineering ; Classical Mechanics ; Control ; Differential equations ; Dynamic stability ; Dynamical Systems ; Engineering ; Hyperbolic functions ; Integral equations ; Mechanical Engineering ; Ordinary differential equations ; Original Paper ; Solitary waves ; Stability analysis ; Vibration</subject><ispartof>Nonlinear dynamics, 2022-02, Vol.107 (3), p.2689-2701</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603</citedby><cites>FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603</cites><orcidid>0000-0001-6883-7788</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>Malik, Sandeep</creatorcontrib><creatorcontrib>Kumar, Sachin</creatorcontrib><creatorcontrib>Das, Amiya</creatorcontrib><title>A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions</title><title>Nonlinear dynamics</title><addtitle>Nonlinear Dyn</addtitle><description>In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the governing equation has been reduced to ordinary differential equations. Further, we have constructed the dark, bright, singular and combo bright-singular soliton solutions via different techniques. The hyperbolic function method, the Kudryashov method and a new version of Kudryashov method are among these techniques. Moreover, by using phase plane theory, we investigate the stability of the corresponding dynamical system.</description><subject>Automotive Engineering</subject><subject>Classical Mechanics</subject><subject>Control</subject><subject>Differential equations</subject><subject>Dynamic stability</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Hyperbolic functions</subject><subject>Integral equations</subject><subject>Mechanical Engineering</subject><subject>Ordinary differential equations</subject><subject>Original Paper</subject><subject>Solitary waves</subject><subject>Stability analysis</subject><subject>Vibration</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kM9KAzEQxoMoWKsv4CngRdHoJLvZJN5K8R8WvKj0FrKbtKR0d9vNLrQ338E39EnMWsGbh-EbZr7fkHwInVK4pgDiJlAKghJgsQQITjZ7aEC5SAjL1HQfDUCxlICC6SE6CmEBAAkDOUB-hM_ZJb0g1peuCr6uzBIXdZn7yln8bN-_Pj7LKNitO9PG9S32Vevmjcn90rfbKxza3xabyG6DD7GxONRxVle9dj0XjtHBzCyDO_nVIXq7v3sdP5LJy8PTeDQhRUJVS6RQuXEunaUyEcpkhQTGlGScW2koh_ifOGBGcqOUlalVnOeW5jYVtMgySIbobHd31dTrzoVWL-quiU8LmmVMppBmSe9iO1fR1CE0bqZXjS9Ns9UUdB-p3kWqY6T6J1K9iVCyg0I0V3PX_J3-h_oGx-J6YA</recordid><startdate>20220201</startdate><enddate>20220201</enddate><creator>Malik, Sandeep</creator><creator>Kumar, Sachin</creator><creator>Das, Amiya</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><orcidid>https://orcid.org/0000-0001-6883-7788</orcidid></search><sort><creationdate>20220201</creationdate><title>A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions</title><author>Malik, Sandeep ; Kumar, Sachin ; Das, Amiya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Automotive Engineering</topic><topic>Classical Mechanics</topic><topic>Control</topic><topic>Differential equations</topic><topic>Dynamic stability</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Hyperbolic functions</topic><topic>Integral equations</topic><topic>Mechanical Engineering</topic><topic>Ordinary differential equations</topic><topic>Original Paper</topic><topic>Solitary waves</topic><topic>Stability analysis</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Malik, Sandeep</creatorcontrib><creatorcontrib>Kumar, Sachin</creatorcontrib><creatorcontrib>Das, Amiya</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central</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>Malik, Sandeep</au><au>Kumar, Sachin</au><au>Das, Amiya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions</atitle><jtitle>Nonlinear dynamics</jtitle><stitle>Nonlinear Dyn</stitle><date>2022-02-01</date><risdate>2022</risdate><volume>107</volume><issue>3</issue><spage>2689</spage><epage>2701</epage><pages>2689-2701</pages><issn>0924-090X</issn><eissn>1573-269X</eissn><abstract>In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the governing equation has been reduced to ordinary differential equations. Further, we have constructed the dark, bright, singular and combo bright-singular soliton solutions via different techniques. The hyperbolic function method, the Kudryashov method and a new version of Kudryashov method are among these techniques. Moreover, by using phase plane theory, we investigate the stability of the corresponding dynamical system.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11071-021-07075-x</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0001-6883-7788</orcidid></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0924-090X |
ispartof | Nonlinear dynamics, 2022-02, Vol.107 (3), p.2689-2701 |
issn | 0924-090X 1573-269X |
language | eng |
recordid | cdi_proquest_journals_2628404630 |
source | Springer Link |
subjects | Automotive Engineering Classical Mechanics Control Differential equations Dynamic stability Dynamical Systems Engineering Hyperbolic functions Integral equations Mechanical Engineering Ordinary differential equations Original Paper Solitary waves Stability analysis Vibration |
title | A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions |
url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-09-21T14%3A56%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20(2+1)-dimensional%20combined%20KdV%E2%80%93mKdV%20equation:%20integrability,%20stability%20analysis%20and%20soliton%20solutions&rft.jtitle=Nonlinear%20dynamics&rft.au=Malik,%20Sandeep&rft.date=2022-02-01&rft.volume=107&rft.issue=3&rft.spage=2689&rft.epage=2701&rft.pages=2689-2701&rft.issn=0924-090X&rft.eissn=1573-269X&rft_id=info:doi/10.1007/s11071-021-07075-x&rft_dat=%3Cproquest_cross%3E2628404630%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-879baee4f48379a6c802298255d8a1502690222a85a99d84d955bd1bd471c6603%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2628404630&rft_id=info:pmid/&rfr_iscdi=true |