English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation andtwo dimensional Benjamin-Ono (2DBO) equation are considered using parabolicfront initial data. Employing a front tracking type ansatz exactly reduces thestudy of DSWs in two space one time (2+1) dimensions to finding DSW solutionsof (1+1) dimensional equations. With this ansatz, the KP and 2DBO equations canbe exactly reduced to cylindrical Korteweg-de Vries (cKdV) and cylindricalBenjamin-Ono (cBO) equations, respectively. Whitham modulation equations whichdescribe DSW evolution in the cKdV and cBO equations are derived in general andRiemann type variables are introduced. DSWs obtained from the numericalsolutions of the corresponding Whitham systems and direct numerical simulationsof the cKdV and cBO equations are compared with excellent agreement obtained.In turn, DSWs obtained from direct numerical simulations of the KP and 2DBOequations are compared with the cKdV and cBO equations, again with remarkableagreement. It is concluded that the (2+1) DSW behavior along parabolic frontscan be effectively described by the DSW solutions of the reduced (1+1)dimensional equations.

Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations