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.Comment: 20 pages, 10 figure
