Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

Yokus A., KAYA D.

International Journal of Modern Physics B, cilt.34, sa.29, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 29
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s0217979220502823
  • Dergi Adı: International Journal of Modern Physics B
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Auto-Backlund transformation method, combined Korteweg de Vries-modified Korteweg de Vries equation, complexly coupled KdV equation, Finite difference method, solitary wave solution
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier-von Neumann stability analysis, the stability of the FDM with the cKdV-mKdV equation is analyzed. The L2 and L8 norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.