Helical solitons in vector modified Korteweg-de Vries equations

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
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4902 Mathematical physics > 490202 Integrable systems (classical and quantum) 51 PHYSICAL SCIENCES > 5106 Nuclear and plasma physics > 510602 Plasma physics; fusion plasmas; electrical discharges 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 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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