Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity
This paper studies the bifurcations of the exact solutions for the time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, for different parameters, there are different kinds of first integrals for the corresponding traveling wave systems. Using the met...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/2/201 |
| _version_ | 1827757348877238272 |
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| author | Wenjing Zhu Zijie Ling Yonghui Xia Min Gao |
| author_facet | Wenjing Zhu Zijie Ling Yonghui Xia Min Gao |
| author_sort | Wenjing Zhu |
| collection | DOAJ |
| description | This paper studies the bifurcations of the exact solutions for the time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, for different parameters, there are different kinds of first integrals for the corresponding traveling wave systems. Using the method of dynamical systems, which is different from the previous works, we obtain the phase portraits of the the corresponding traveling wave systems. In addition, we derive the exact parametric representations of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions, peakon solutions, periodic peakon solutions and compacton solutions under different parameter conditions. |
| first_indexed | 2024-03-11T08:48:27Z |
| format | Article |
| id | doaj.art-fe189fdbd9a44558b1490dca98b2bfe0 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:48:27Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-fe189fdbd9a44558b1490dca98b2bfe02023-11-16T20:37:24ZengMDPI AGFractal and Fractional2504-31102023-02-017220110.3390/fractalfract7020201Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law NonlinearityWenjing Zhu0Zijie Ling1Yonghui Xia2Min Gao3School of Mathematics, China Jiliang University, Hangzhou 310018, ChinaSchool of Mathematics, China Jiliang University, Hangzhou 310018, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaSchool of Mathematics, China Jiliang University, Hangzhou 310018, ChinaThis paper studies the bifurcations of the exact solutions for the time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, for different parameters, there are different kinds of first integrals for the corresponding traveling wave systems. Using the method of dynamical systems, which is different from the previous works, we obtain the phase portraits of the the corresponding traveling wave systems. In addition, we derive the exact parametric representations of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions, peakon solutions, periodic peakon solutions and compacton solutions under different parameter conditions.https://www.mdpi.com/2504-3110/7/2/201bifurcationsphase portraitsexact solutions |
| spellingShingle | Wenjing Zhu Zijie Ling Yonghui Xia Min Gao Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity Fractal and Fractional bifurcations phase portraits exact solutions |
| title | Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity |
| title_full | Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity |
| title_fullStr | Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity |
| title_full_unstemmed | Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity |
| title_short | Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity |
| title_sort | bifurcations and the exact solutions of the time space fractional complex ginzburg landau equation with parabolic law nonlinearity |
| topic | bifurcations phase portraits exact solutions |
| url | https://www.mdpi.com/2504-3110/7/2/201 |
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