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


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.

Statistics for USQ ePrint 34847
Statistics for this ePrint Item
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

Actions (login required)

View Item Archive Repository Staff Only