Nonlinear modulation of periodic waves in the cylindrical Gardner equation

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Aslanova G., Ahmetolan S. , Demirci A.

PHYSICAL REVIEW E, vol.102, no.5, 2020 (Journal Indexed in SCI) identifier identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 102 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.1103/physreve.102.052215
  • Title of Journal : PHYSICAL REVIEW E


The propagation of dispersive shock waves (DSWs) is investigated in the cylindrical Gardner (cG) equation, which is obtained by employing a similarity reduction to the two-space one-time (2+1) dimensional Gardner-Kadomtsev-Petviashvili (Gardner-KP) equation. We consider the steplike initial condition along a parabolic front. Then, the cG-Whitham modulation system, which is a description of DSW evolution in the cG equation, in terms of appropriate Riemann-type variables is derived. Our study is supported by numerical simulations. The comparison is given between the direct numerical solution of the cG equation and the DSW solution obtained from the numerical solution of the Whitham system. According to this comparison, a good agreement is found between the solutions.