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arXiv · 1805.09074

Helical solitons in vector modified Korteweg-de Vries equations

Dmitry E. Pelinovsky·Yury A. Stepanyants
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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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Dmitry E. Pelinovsky, Yury A. Stepanyants. 2018-09-23. Helical solitons in vector modified Korteweg-de Vries equations. https://doi.org/10.1016/j.physleta.2018.08.015

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