English

Soliton Generation and Multiple Phases in Dispersive Shock and Rarefaction Wave Interaction

Pattern Formation and Solitons 2013-01-08 v1 Exactly Solvable and Integrable Systems

Abstract

Interactions of dispersive shock (DSWs) and rarefaction waves (RWs) associated with the Korteweg-de Vries equation are shown to exhibit multiphase dynamics and isolated solitons. There are six canonical cases: one is the interaction of two DSWs which exhibit a transient two-phase solution, but evolve to a single phase DSW for large time; two tend to a DSW with either a small amplitude wave train or a finite number of solitons, which can be determined analytically; two tend to a RW with either a small wave train or a finite number of solitons; finally, one tends to a pure RW.

Keywords

Cite

@article{arxiv.0904.3160,
  title  = {Soliton Generation and Multiple Phases in Dispersive Shock and Rarefaction Wave Interaction},
  author = {M. J. Ablowitz and D. E. Baldwin and M. A. Hoefer},
  journal= {arXiv preprint arXiv:0904.3160},
  year   = {2013}
}

Comments

4 pages, 6 figures

R2 v1 2026-06-21T12:53:24.745Z