Analytic solutions for the (2+1)-dimensional generalized sine-Gordon equations in nonlinear optics
The (2+1)-dimensional generalized sine-Gordon equations can be used to describe the propagation of femtosecond laser pulse in a systems of two-level atoms. In this paper, bilinear forms of the equations have been constructed through variable transformation and Bell polynomial. Based on the bilinear...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2018-09, Vol.76 (6), p.1535-1543 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Meng, Gao-Qing Pan, Yu-Song Tan, Hao-feng Xie, Xi-Yang |
| description | The (2+1)-dimensional generalized sine-Gordon equations can be used to describe the propagation of femtosecond laser pulse in a systems of two-level atoms. In this paper, bilinear forms of the equations have been constructed through variable transformation and Bell polynomial. Based on the bilinear method and truncated Painlevé expansion, multi-soliton and quasi-periodic peakon solutions for such a system are derived, respectively. Overtaking elastic interactions between the two solitons and among the three solitons have been found. It is presented that the soliton with the smaller amplitude can travel faster than the larger one. Apart from the soliton, other type of nonlinear wave propagating in the systems of two-level atoms has been displayed, namely the quasi-periodic peakon. The peakon oscillates in both space and time, while its left and right derivatives at peak point are relatively large, which means the electric-field intensity of the femtosecond laser pulse is rather strong. |
| doi_str_mv | 10.1016/j.camwa.2018.07.005 |
| format | Article |
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The peakon oscillates in both space and time, while its left and right derivatives at peak point are relatively large, which means the electric-field intensity of the femtosecond laser pulse is rather strong.</description><subject>Bell polynomial</subject><subject>Bilinear method</subject><subject>Combinatorial analysis</subject><subject>Dimensional analysis</subject><subject>Femtosecond pulses</subject><subject>Generalized sine-Gordon equation</subject><subject>Linear equations</subject><subject>Mathematical analysis</subject><subject>Multi-soliton solutions</subject><subject>Nonlinear equations</subject><subject>Nonlinear optics</subject><subject>Optics</subject><subject>Peakon</subject><subject>Polynomials</subject><subject>Propagation</subject><subject>Pulse propagation</subject><subject>Solitary waves</subject><subject>Truncated Painlevé expansion</subject><subject>Wave propagation</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwC1gssYBQgj-S2BkYqgoKUiUWmC3HuYCr1G7tBFR-PS5lZrrhvefV3YPQJSU5JbS6W-VGr790zgiVORE5IeURmlApeCaqSh6jCZG1zChj9BSdxbgihBSckQlqZk73u8EaHH0_Dta7iDsf8PAB-Jrd0pustWtwMQW6x-_gIOjefkOLo3WQLXxovcOwHfWBtQ477_qU6YD9JhXHc3TS6T7Cxd-corfHh9f5U7Z8WTzPZ8vMcE6HrOkMrwtWNBXlgtRVAaIEyRqha6YFMZ0oW1PXrZASwGitO0lLLVohupKLmvIpujr0boLfjhAHtfJjSGdHxSitU3clZNrihy0TfIwBOrUJdq3DTlGi9jLVSv3KVHuZigiVZCbq_kBBeuDTQlDRWHAGWhvADKr19l_-BzbXfu4</recordid><startdate>20180915</startdate><enddate>20180915</enddate><creator>Meng, Gao-Qing</creator><creator>Pan, Yu-Song</creator><creator>Tan, Hao-feng</creator><creator>Xie, Xi-Yang</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</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>20180915</creationdate><title>Analytic solutions for the (2+1)-dimensional generalized sine-Gordon equations in nonlinear optics</title><author>Meng, Gao-Qing ; Pan, Yu-Song ; Tan, Hao-feng ; Xie, Xi-Yang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-bfc39424b61370964e75e82b7a92a70cf75dc99d788eecaaaf815a7d77f537913</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Bell polynomial</topic><topic>Bilinear method</topic><topic>Combinatorial analysis</topic><topic>Dimensional analysis</topic><topic>Femtosecond pulses</topic><topic>Generalized sine-Gordon equation</topic><topic>Linear equations</topic><topic>Mathematical analysis</topic><topic>Multi-soliton solutions</topic><topic>Nonlinear equations</topic><topic>Nonlinear optics</topic><topic>Optics</topic><topic>Peakon</topic><topic>Polynomials</topic><topic>Propagation</topic><topic>Pulse propagation</topic><topic>Solitary waves</topic><topic>Truncated Painlevé expansion</topic><topic>Wave propagation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Meng, Gao-Qing</creatorcontrib><creatorcontrib>Pan, Yu-Song</creatorcontrib><creatorcontrib>Tan, Hao-feng</creatorcontrib><creatorcontrib>Xie, Xi-Yang</creatorcontrib><collection>CrossRef</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>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Meng, Gao-Qing</au><au>Pan, Yu-Song</au><au>Tan, Hao-feng</au><au>Xie, Xi-Yang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytic solutions for the (2+1)-dimensional generalized sine-Gordon equations in nonlinear optics</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2018-09-15</date><risdate>2018</risdate><volume>76</volume><issue>6</issue><spage>1535</spage><epage>1543</epage><pages>1535-1543</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>The (2+1)-dimensional generalized sine-Gordon equations can be used to describe the propagation of femtosecond laser pulse in a systems of two-level atoms. 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| ispartof | Computers & mathematics with applications (1987), 2018-09, Vol.76 (6), p.1535-1543 |
| issn | 0898-1221 1873-7668 |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Bell polynomial Bilinear method Combinatorial analysis Dimensional analysis Femtosecond pulses Generalized sine-Gordon equation Linear equations Mathematical analysis Multi-soliton solutions Nonlinear equations Nonlinear optics Optics Peakon Polynomials Propagation Pulse propagation Solitary waves Truncated Painlevé expansion Wave propagation |
| title | Analytic solutions for the (2+1)-dimensional generalized sine-Gordon equations in nonlinear optics |
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