Helical solitons in vector modified Korteweg-de Vries equations

Pelinovsky, Dmitry E. and Stepanyants, Yury A. (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 / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 16 Oct 2018 06:14
Last Modified: 26 Oct 2018 05:05
Uncontrolled Keywords: plasma waves; particle-spring chains; vector modified Korteweg-deVriesequation; helical solitons
Fields of Research : 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 Objective: 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: 10.1016/j.physleta.2018.08.015
URI: http://eprints.usq.edu.au/id/eprint/34847

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