Nonlocal symmetries and new interaction waves of the variable-coefficient modified Korteweg–de Vries equation in fluid-filled elastic tubes
The Lax pair is developed to construct nonlocal symmetries of the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation in fluid-filled elastic tubes. To construct new exact solutions with the nonlocal symmetry, we use the localization approach, which can transform the problem of nonloc...
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| Veröffentlicht in: | European physical journal plus Jg. 137; H. 7; S. 814 |
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| Abstract | The Lax pair is developed to construct nonlocal symmetries of the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation in fluid-filled elastic tubes. To construct new exact solutions with the nonlocal symmetry, we use the localization approach, which can transform the problem of nonlocal symmetries to Lie point symmmetries. Furthermore, using the classic Lie group reduction method some group invariant solutions of the vc-mKdV equation are obtained. For some interesting solutions, the soliton-cnoidal waves are discussed through the graphical analysis. |
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| AbstractList | The Lax pair is developed to construct nonlocal symmetries of the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation in fluid-filled elastic tubes. To construct new exact solutions with the nonlocal symmetry, we use the localization approach, which can transform the problem of nonlocal symmetries to Lie point symmmetries. Furthermore, using the classic Lie group reduction method some group invariant solutions of the vc-mKdV equation are obtained. For some interesting solutions, the soliton-cnoidal waves are discussed through the graphical analysis. |
| ArticleNumber | 814 |
| Author | Wu, Jian-Wen Lin, Ji He, Jun-Tao |
| Author_xml | – sequence: 1 givenname: Jian-Wen orcidid: 0000-0001-7014-6660 surname: Wu fullname: Wu, Jian-Wen organization: Department of Physics, Zhejiang Normal University – sequence: 2 givenname: Jun-Tao surname: He fullname: He, Jun-Tao organization: Department of Physics, Zhejiang Normal University – sequence: 3 givenname: Ji surname: Lin fullname: Lin, Ji email: linji@zjnu.edu.cn organization: Department of Physics, Zhejiang Normal University |
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| Cites_doi | 10.1016/j.camwa.2018.07.018 10.1103/PhysRevE.84.026606 10.1016/j.matcom.2010.02.001 10.1002/mma.2561 10.1016/j.cam.2005.10.043 10.1088/0031-8949/89/12/125203 10.1016/j.aml.2020.107004 10.1088/0256-307X/31/1/010201 10.1016/S0020-7225(03)00284-2 10.1088/1402-4896/ab8d02 10.1016/j.joes.2021.09.003 10.1007/s11071-018-4051-2 10.1016/j.cnsns.2010.07.021 10.1103/PhysRevE.85.056607 10.1515/phys-2018-0073 10.1016/j.aml.2018.08.023 10.1007/s40840-018-0668-z 10.1515/zna-2016-0078 10.1017/CBO9780511623998 10.1364/OE.20.007469 10.1007/s11071-017-3475-4 10.1016/j.jmmm.2020.166590 10.1088/1751-8113/45/15/155209 10.1016/j.aop.2008.04.012 10.1088/0305-4470/39/20/L08 10.1088/0305-4470/24/10/003 10.1088/0253-6102/70/2/119 10.1016/j.wavemoti.2021.102719 10.1007/s11071-016-2998-4 10.1143/JPSJ.50.338 10.1088/1402-4896/aacd42 10.1016/j.wavemoti.2014.07.012 10.1007/978-0-387-68028-6 10.1088/0305-4470/30/5/004 10.1016/j.wavemoti.2018.08.008 10.1016/j.aml.2020.106326 10.1103/PhysRevE.77.036605 10.1088/1572-9494/abf552 10.1016/j.aml.2019.02.028 |
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