Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations

Özdemir N., Demirci A., Ahmetolan S.

International Journal of Theoretical Physics, vol.63, no.12, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 12
  • Publication Date: 2024
  • Doi Number: 10.1007/s10773-024-05841-2
  • Journal Name: International Journal of Theoretical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Dispersive shock waves, Focusing and defocusing cylindrical modified KdV equations, Riemann problem classification, Whitham modulation theory
  • Marmara University Affiliated: No

Abstract

This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.