Wave propagation and bifurcation phenomena in the generalized equal width equation with dual-power nonlinearity

Saha A., ERSOY HEPSON Ö., Ak T., Osman M. S., Chettri Y., Ghatani Y.

Mathematics and Computers in Simulation, cilt.249, ss.411-427, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 249
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.matcom.2026.05.030
  • Dergi Adı: Mathematics and Computers in Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, Public Affairs Index, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
  • Sayfa Sayıları: ss.411-427
  • Anahtar Kelimeler: Bifurcation, Collocation, Phase portrait, Traveling waves, Unified method
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

This study introduces a generalized form of the Equal Width (EW) equation incorporating dual power nonlinearity. Analytical and numerical investigations are conducted using the unified method and the collocation method respectively to examine the solution behavior and structural properties of the proposed model. Using a suitable transformation, the generalized EW equation is transformed into a nonlinear dynamical system. Through phase-plane analysis, the qualitative behavior of the nonlinear waves is explored considering all possible cases. The existence of various nonlinear and supernonlinear trajectories, such as nonlinear heteroclinic orbits, nonlinear peak-type and valley-type homoclinic orbits, nonlinear periodic orbits, supernonlinear periodic orbits, and supernonlinear heteroclinic orbits, is reported through different phase portraits. Furthermore, various exact wave solutions, including solitary, kink, and antikink waves, are obtained. These results provide new insights into the dynamics of shallow-water waves described by the generalized EW equation with dual power nonlinearity.