Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation
The main attention of this study is focused on the interaction dynamics of breather, and hybrid solitons and breather for an extended generalization of Vakhnenko equation. The general form of the N -order auxiliary function is first derived by the Hirota bilinear method. Then, the N -order solutions...
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| Published in | Nonlinear dynamics Vol. 102; no. 3; pp. 1787 - 1799 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.11.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0924-090X 1573-269X 1573-269X |
| DOI | 10.1007/s11071-020-06024-4 |
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| Abstract | The main attention of this study is focused on the interaction dynamics of breather, and hybrid solitons and breather for an extended generalization of Vakhnenko equation. The general form of the
N
-order auxiliary function is first derived by the Hirota bilinear method. Then, the
N
-order solutions can be obtained. When
N
≥
2
, the loop-like breather may emerge by taking the dispersion coefficients as conjugate complex number. The breather is like a magical spring with good elasticity, changeable period and thickness. Furthermore, novel interaction features between breathers, between soliton/solitons and breather/breathers, are observed by visualizing method. The results show that there are abundant dynamics during the interactions, such as elastic collision, phase shift, amplitude amplification, collapse and bulge effect. |
|---|---|
| AbstractList | The main attention of this study is focused on the interaction dynamics of breather, and hybrid solitons and breather for an extended generalization of Vakhnenko equation. The general form of the N-order auxiliary function is first derived by the Hirota bilinear method. Then, the N-order solutions can be obtained. When N≥2, the loop-like breather may emerge by taking the dispersion coefficients as conjugate complex number. The breather is like a magical spring with good elasticity, changeable period and thickness. Furthermore, novel interaction features between breathers, between soliton/solitons and breather/breathers, are observed by visualizing method. The results show that there are abundant dynamics during the interactions, such as elastic collision, phase shift, amplitude amplification, collapse and bulge effect. The main attention of this study is focused on the interaction dynamics of breather, and hybrid solitons and breather for an extended generalization of Vakhnenko equation. The general form of the N -order auxiliary function is first derived by the Hirota bilinear method. Then, the N -order solutions can be obtained. When N ≥ 2 , the loop-like breather may emerge by taking the dispersion coefficients as conjugate complex number. The breather is like a magical spring with good elasticity, changeable period and thickness. Furthermore, novel interaction features between breathers, between soliton/solitons and breather/breathers, are observed by visualizing method. The results show that there are abundant dynamics during the interactions, such as elastic collision, phase shift, amplitude amplification, collapse and bulge effect. |
| Author | Ma, Yu-Lan Li, Bang-Qing |
| Author_xml | – sequence: 1 givenname: Bang-Qing surname: Li fullname: Li, Bang-Qing organization: Academy of Systems Science, Beijing Technology and Business University, School of Computer, Beijing Technology and Business University – sequence: 2 givenname: Yu-Lan orcidid: 0000-0003-3205-1729 surname: Ma fullname: Ma, Yu-Lan email: mayl@th.btbu.edu.cn organization: School of Mathematics and Statistics, Beijing Technology and Business University |
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| Keywords | Hirota bilinear method General Extended generalization of Vakhnenko equation (EGVE) Interactions dynamics Loop-like soliton order auxiliary function Loop-like breather |
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| SubjectTerms | Automotive Engineering Breathers Classical Mechanics Complex numbers Control Dynamical Systems Elastic scattering Engineering Mechanical Engineering Original Paper Solitary waves Vibration |
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| Title | Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation |
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