Soliton generation and multiple phases in dispersive shock and rarefaction wave interaction.
Interactions of dispersive shock waves (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 that 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.
Ablowitz
M J
MJ
Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
Baldwin
D E
DE
Hoefer
M A
MA