The Dynamics on Soliton Molecules and Soliton Bifurcation for an Extended Generalization of Vakhnenko Equation
Vakhnenko-type equations play a critical role in nonlinear electromagnetic and optical fiber applications. In this article, we present a new advancement in high-frequency wave propagation in electromagnetic and optical fiber applications by investigating an extended generalization of the Vakhnenko e...
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| Vydáno v: | Qualitative theory of dynamical systems Ročník 23; číslo 3 |
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01.07.2024
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| ISSN: | 1575-5460, 1662-3592 |
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| Abstract | Vakhnenko-type equations play a critical role in nonlinear electromagnetic and optical fiber applications. In this article, we present a new advancement in high-frequency wave propagation in electromagnetic and optical fiber applications by investigating an extended generalization of the Vakhnenko equation. In our study, we employ the bilinear method and introduce an auxiliary function that combines exponential and cosine functions. By utilizing this approach, we are able to derive two distinct sets of analytical solutions for the equation. By choosing suitable parameters involved in the solutions, we identify the presence of soliton molecules and soliton bifurcation in the equation. Furthermore, for the soliton molecules, we note the existence of two distinct types of phase transitions: (i) a transition from soliton molecules to loop-like breathers, and (ii) a transition from soliton molecules to intersection solitons. Regarding soliton bifurcation, we observe phase transitions among loop-like, cusp-like, and peak-like solitons. Moreover, the results of this study illuminate that the structures of all solitons, within the context of soliton molecules and soliton bifurcation, remain stable throughout the phase transitions. This stability carries considerable significance for practical applications. |
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| AbstractList | Vakhnenko-type equations play a critical role in nonlinear electromagnetic and optical fiber applications. In this article, we present a new advancement in high-frequency wave propagation in electromagnetic and optical fiber applications by investigating an extended generalization of the Vakhnenko equation. In our study, we employ the bilinear method and introduce an auxiliary function that combines exponential and cosine functions. By utilizing this approach, we are able to derive two distinct sets of analytical solutions for the equation. By choosing suitable parameters involved in the solutions, we identify the presence of soliton molecules and soliton bifurcation in the equation. Furthermore, for the soliton molecules, we note the existence of two distinct types of phase transitions: (i) a transition from soliton molecules to loop-like breathers, and (ii) a transition from soliton molecules to intersection solitons. Regarding soliton bifurcation, we observe phase transitions among loop-like, cusp-like, and peak-like solitons. Moreover, the results of this study illuminate that the structures of all solitons, within the context of soliton molecules and soliton bifurcation, remain stable throughout the phase transitions. This stability carries considerable significance for practical applications. |
| ArticleNumber | 137 |
| Author | Ma, Yu-Lan Li, Bang-Qing |
| Author_xml | – sequence: 1 givenname: Yu-Lan surname: Ma fullname: Ma, Yu-Lan organization: School of Mathematics and Statistics, Beijing Technology and Business University – sequence: 2 givenname: Bang-Qing surname: Li fullname: Li, Bang-Qing email: libq@th.btbu.edu.cn organization: School of Computer and Artificial Intelligence, Beijing Technology and Business University, Academy of Systems Science, Beijing Technology and Business University |
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| CitedBy_id | crossref_primary_10_1007_s44198_025_00317_1 crossref_primary_10_1007_s12346_024_01163_0 crossref_primary_10_1007_s12346_024_01103_y crossref_primary_10_1016_j_optlastec_2025_112647 crossref_primary_10_1007_s12346_024_01125_6 crossref_primary_10_1007_s12346_024_01176_9 crossref_primary_10_1002_mma_10764 crossref_primary_10_1016_j_matcom_2025_07_058 crossref_primary_10_1016_j_optlastec_2024_112065 crossref_primary_10_1080_00207160_2024_2435017 crossref_primary_10_1007_s12346_025_01310_1 crossref_primary_10_1007_s12346_025_01241_x crossref_primary_10_1016_j_cjph_2024_12_006 |
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| Keywords | Extended generalization of Vakhnenko equation Bilinear method Soliton bifurcation Soliton molecules Phase transition |
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| Title | The Dynamics on Soliton Molecules and Soliton Bifurcation for an Extended Generalization of Vakhnenko Equation |
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