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, cilt.63, sa.12, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: 12
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s10773-024-05841-2
  • Dergi Adı: International Journal of Theoretical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Dispersive shock waves, Focusing and defocusing cylindrical modified KdV equations, Riemann problem classification, Whitham modulation theory
  • Marmara Üniversitesi Adresli: Hayır

Özet

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.