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

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

2009-04-21

arxiv.org/abs/0904.3160v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 6 figures

Scientific paper

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.

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