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Published on: February 13, 2018
Propagation of generalized Korteweg-de Vries solitons along large-scale waves
1Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia; Moscow Institute of Physics and Technology, Institutsky Lane 9, Dolgoprudny, Moscow Region 141700, Russia; and Skolkovo Institute of Science and Technology, Skolkovo, Moscow 143026, Russia.
Abstract:
We consider propagation of solitons along large-scale background waves in the generalized Korteweg-de Vries (gKdV) equation theory when the width of the soliton is much smaller than the characteristic size of the background wave. Due to this difference in scales, the soliton's motion does not affect the dispersionless evolution of the background wave. We obtained the Hamilton equations for soliton's motion and derived simple relationships which express the soliton's velocity in terms of a local value of the background wave. Solitons' paths obtained by integration of these relationships agree very well with the exact numerical solutions of the gKdV equation.
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