Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas
In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindri...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9075823 |
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| author | Quansheng Liu Liguo Chen |
| author_facet | Quansheng Liu Liguo Chen |
| author_sort | Quansheng Liu |
| collection | DOAJ |
| description | In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speed λ, electron number density (through β3) and the fractional order α,β,ω on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed. |
| format | Article |
| id | doaj-art-40bb2e2908bf4e61beb01cf77ae9ab37 |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-40bb2e2908bf4e61beb01cf77ae9ab372025-08-20T02:39:13ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/90758239075823Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic PlasmasQuansheng Liu0Liguo Chen1School of Mathematical Sciences, Inner Mongolia University, Hohhot 010070, ChinaSchool of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, ChinaIn this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speed λ, electron number density (through β3) and the fractional order α,β,ω on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.http://dx.doi.org/10.1155/2020/9075823 |
| spellingShingle | Quansheng Liu Liguo Chen Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas Complexity |
| title | Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas |
| title_full | Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas |
| title_fullStr | Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas |
| title_full_unstemmed | Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas |
| title_short | Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas |
| title_sort | time space fractional model for complex cylindrical ion acoustic waves in ultrarelativistic plasmas |
| url | http://dx.doi.org/10.1155/2020/9075823 |
| work_keys_str_mv | AT quanshengliu timespacefractionalmodelforcomplexcylindricalionacousticwavesinultrarelativisticplasmas AT liguochen timespacefractionalmodelforcomplexcylindricalionacousticwavesinultrarelativisticplasmas |