Modulated periodic wavetrains in the spherical Gardner equation

Aslanova G., Demirci A. , Ahmetolan S.

Wave Motion, vol.109, 2022 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 109
  • Publication Date: 2022
  • Doi Number: 10.1016/j.wavemoti.2021.102844
  • Title of Journal : Wave Motion
  • Keywords: Dispersive shock waves, Gardner–KP equation, Whitham modulation theory


© 2021 Elsevier B.V.The spherical Gardner (sG) equation is derived by reducing the (3+1)-dimensional Gardner–Kadomtsev–Petviashvili (Gardner–KP) equation with a similarity reduction. As a special case, the step-like initial condition is considered along a paraboloid front. By applying a multiple-scale expansion, a system of first order partial differential equations for the slowly varying parameters of a periodic wavetrain is obtained. The corresponding modulation system is transformed into a simpler form with the help of Riemann type variables. This basic form is important to investigate the dispersive shock wave (DSW) phenomena in the sG equation. DSW solution is also compared with the numerical solution of the sG equation and good agreement is found between these solutions.