Pelinovsky, Dmitry E. and Stepanyants, Yury A. 
ORCID: https://orcid.org/0000-0003-4546-0310
(2018)
Helical solitons in vector modified Korteweg-de Vries equations.
Physics Letters A, 382 (44).
pp. 3165-3171.
ISSN 0375-9601
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.
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| Item Type: | Article (Commonwealth Reporting Category C) |
|---|---|
| Refereed: | Yes |
| Item Status: | Live Archive |
| Additional Information: | Permanent restricted access to Published version in accordance with the copyright policy of the publisher. |
| Faculty/School / Institute/Centre: | Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019) |
| Faculty/School / Institute/Centre: | Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019) |
| Date Deposited: | 16 Oct 2018 06:14 |
| Last Modified: | 15 Feb 2021 23:33 |
| Uncontrolled Keywords: | plasma waves; particle-spring chains; vector modified Korteweg-deVriesequation; helical solitons |
| Fields of Research (2008): | 01 Mathematical Sciences > 0105 Mathematical Physics > 010502 Integrable Systems (Classical and Quantum) 02 Physical Sciences > 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics > 020204 Plasma Physics; Fusion Plasmas; Electrical Discharges 01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics |
| Socio-Economic Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| Identification Number or DOI: | https://doi.org/10.1016/j.physleta.2018.08.015 |
| URI: | http://eprints.usq.edu.au/id/eprint/34847 |
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