Modulated periodic wavetrains in the spherical Gardner equation

Aslanova G., Demirci A., Ahmetolan S.

Wave Motion, vol.109, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 109
  • Publication Date: 2022
  • Doi Number: 10.1016/j.wavemoti.2021.102844
  • Journal Name: Wave Motion
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Geobase, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Whitham modulation theory, Dispersive shock waves, Gardner-KP equation, Whitham modulation theory, Dispersive shock waves, Gardner-KP equation, KADOMTSEV-PETVIASHVILI, MODIFIED KORTEWEG, DYNAMICS
  • Istanbul Technical University Affiliated: Yes


© 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.