Refraction of dispersive shock waves

G. A. El*, V. V. Khodorovskii, A. M. Leszczyszyn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
9 Downloads (Pure)


We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.

Original languageEnglish
Pages (from-to)1567-1587
Number of pages21
JournalPhysica D: Nonlinear Phenomena
Issue number18
Early online date19 Jun 2012
Publication statusPublished - 15 Sept 2012
Externally publishedYes


Dive into the research topics of 'Refraction of dispersive shock waves'. Together they form a unique fingerprint.

Cite this