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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