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

Asit Saha, Özlem Ersoy Hepson, Turgut Ak, Mohamed S. Osman, Yogesh Chettri and Yogen Ghatani

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 411-427

Abstract: 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.

Keywords: Traveling waves; Unified method; Collocation; Bifurcation; Phase portrait (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:411-427

DOI: 10.1016/j.matcom.2026.05.030

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