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

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Ablowitz, M. J.
Baldwin, D. E.
Hoefer, M. A.
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Abstract
Description
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.
Comment: 4 pages, 6 figures
Keywords
Nonlinear Sciences - Pattern Formation and Solitons, Nonlinear Sciences - Exactly Solvable and Integrable Systems
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