Solitons, and quantitative analysis of the (2+1) dimensional Boussinesq equation in a dispersive medium
Rendiconti Lincei, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1007/s12210-026-01453-6
- Journal Name: Rendiconti Lincei
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, zbMATH, Natural Science Collection (ProQuest), Biological Science Database (ProQuest), Earth, Atmospheric, & Aquatic Science Collection (ProQuest)
- Keywords: Bifurcation theory, Hirota bilinear method, Lump waves, Sensitivity analysis, Shallow water waves, Soliton solutions, Stability analysis, The (2+1)-dimensional boussinesq equation
- Yıldız Technical University Affiliated: No
Abstract
The (2+1)-dimensional Boussinesq equation describes complex wave propagation in shallow water with varying amplitudes, where dispersion and nonlinearity are important factors. The equation captures wave interactions in multiple dimensions. The Hirota bilinear method and the extended hyperbolic function approach are used to construct lump wave solutions, their interactions with periodic, strip and double-strip waves, and traveling wave solutions. Stability analysis is carried out to determine whether the solutions develop singularities or remain bounded. Bifurcation theory and sensitivity analysis for dynamical systems are applied to obtain phase diagrams of the governing model. Bifurcation theory of planar dynamical systems is also used to examine the model’s qualitative analysis. Three-dimensional graphical representations of the exact solutions show periodic features such dark V-shaped, singular bell-shaped, bright, unique periodic, and periodic soliton solutions. The findings provide analytical insight into the nonlinear dynamics and stability features of the model. Both approaches highlight the rich solution structure and its applications under various physical conditions.