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

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