Propagation of generalized Korteweg-de Vries solitons along large-scale waves
arXiv:2307.12321 · doi:10.1103/PhysRevE.108.054205
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 mach 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.
arXiv comment7 pages, 2 figures
References in corpus (7)
- Motion of dark solitons in trapped Bose-Einstein condensates
- Resolution of a shock in hyperbolic systems modified by weak dispersion
- Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
- Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse
- Motion of dark solitons in a non-uniform flow of Bose-Einstein condensate
- Asymptotic theory of not completely integrable soliton equations
- Propagation of wave packets along intensive simple waves