## Abstract

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).

Original language | English |
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Article number | 129051 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 483 |

DOIs | |

Publication status | Published - 28 Sept 2023 |

### Bibliographical note

Publisher Copyright:© 2023 Elsevier B.V.

### Funding

We would like to thank the referees for their constructive comments and recommendations. The first author was supported by the Scientific and Technological Research Council of Turkey (TUBITAK Programme, 2211 ). This research was supported by the Istanbul Technical University Office of Scientific Research Projects (ITU BAPSIS), under grant TGA-2018-41318 . We thank D.E. Baldwin for MATLAB codes of the version of the ETDRK4 method that we use in the study.

Funders | Funder number |
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Türkiye Bilimsel ve Teknolojik Araştırma Kurumu | |

Istanbul Teknik Üniversitesi | TGA-2018-41318 |

## Keywords

- Spherical reductions
- Undular bore solution
- Whitham modulation theory