Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations


Ablowitz M. J., Demirci A., MA Y.

PHYSICA D-NONLINEAR PHENOMENA, cilt.333, ss.84-98, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 333
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.physd.2016.01.013
  • Dergi Adı: PHYSICA D-NONLINEAR PHENOMENA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.84-98
  • Anahtar Kelimeler: Dispersive shock waves, Kadomtsev-Petviashvili equation, Two dimensional Benjamin-Ono equation, KORTEWEG-DEVRIES EQUATION, SOLITARY WAVES, INTERNAL WAVES, WATER-WAVES, GREAT DEPTH, EVOLUTION, FLUIDS, LIMIT, TRANSFORM
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations. (C) 2016 Elsevier B.V. All rights reserved.