Undular bores in the (3+1) dimensional mKP equation

Özdemir N., Demirci A., Ahmetolan S.

Physics Letters, Section A: General, Atomic and Solid State Physics, vol.483, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 483
  • Publication Date: 2023
  • Doi Number: 10.1016/j.physleta.2023.129051
  • Journal Name: Physics Letters, Section A: General, Atomic and Solid State Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Chemical Abstracts Core, Communication Abstracts, Compendex, INSPEC, Metadex, Philosopher's Index, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Spherical reductions, Undular bore solution, Whitham modulation theory
  • Istanbul Technical University Affiliated: Yes


Undular bore (dispersive shock wave) solutions in the (3+1) dimensional modified Kadomtsev-Petviashvili (mKP) equation for step type initial condition along a paraboloid type wavefront are found. Then, using a suitable solution form for the (3+1) dimensional mKP equation, it is reduced to the (1+1) dimensional focusing spherical mKdV (smKdV) and defocusing spherical mKdV (smKdV(d)) equations. Next, the Whitham modulation equations of the smKdV and smKdV(d) equations are found in terms of Riemann variables. Numerical solutions of the derived modulation equations are obtained. Also, an error analysis is performed for direct numerical solutions of both smKdV and smKdV(d).