Physics Letters, Section A: General, Atomic and Solid State Physics, vol.483, 2023 (SCI-Expanded)
Article / Article
Physics Letters, Section A: General, Atomic and Solid State Physics
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
Spherical reductions, Undular bore solution, Whitham modulation theory
Istanbul Technical University Affiliated:
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).