Helical solitons in vector modified Korteweg-de Vries equations
Article
Article Title | Helical solitons in vector modified Korteweg-de Vries equations |
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ERA Journal ID | 1023 |
Article Category | Article |
Authors | Pelinovsky, Dmitry E. (Author) and Stepanyants, Yury A. (Author) |
Journal Title | Physics Letters A |
Physics Letters A: General Physics, Nonlinear Science, Statistical Physics, Atomic, Molecular and Cluster Physics, Plasma and Fluid Physics, Condensed Matter, Cross-disciplinary Physics, Biological Physics, Nanosciences, Quantum Physics | |
Journal Citation | 382 (44), pp. 3165-3171 |
Number of Pages | 7 |
Year | 2018 |
Place of Publication | Netherlands |
ISSN | 0375-9601 |
1873-2429 | |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.physleta.2018.08.015 |
Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0375960118308879 |
Abstract | We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations. |
Keywords | plasma waves; particle-spring chains; vector modified Korteweg-deVriesequation; helical solitons |
ANZSRC Field of Research 2020 | 490202. Integrable systems (classical and quantum) |
510602. Plasma physics; fusion plasmas; electrical discharges | |
490109. Theoretical and applied mechanics | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Nizhny Novgorod State Technical University, Russia |
School of Agricultural, Computational and Environmental Sciences | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q4xx0/helical-solitons-in-vector-modified-korteweg-de-vries-equations
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