Logarithmic Solitons of the Tzitzéica–Dodd–Bullough Equation: Exact Solutions and Stability Analysis
The 2nd International Online Conference on Mathematics and Applications (IOCMA 2026), Aarau, İsviçre, 10 - 12 Haziran 2026, ss.1-9, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Doi Numarası: 10.3390/cmsf2026015017
- Basıldığı Şehir: Aarau
- Basıldığı Ülke: İsviçre
- Sayfa Sayıları: ss.1-9
- İstanbul Ticaret Üniversitesi Adresli: Evet
Özet
This work derives exact analytical solutions to the nonlinear Tzitzéica–Dodd–Bullough (TDB) equation, which models wave phenomena in differential geometry, plasma physics, and nonlinear field theory. The -expansion method is employed, using a traveling wave ansatz to convert the governing partial differential equation (PDE) into an ordinary differential equation (ODE), which is then solved systematically. The resulting solutions take logarithmic forms and exhibit a variety of wave structures, including solitary waves, periodic oscillations, and singular profiles. Parameter dependence of wave amplitude and localization is also examined. A linear stability analysis reveals that all solutions are neutrally stable, with modulational stability requiring . The results confirm that the -expansion method is a reliable and effective tool for treating exponential nonlinearities. The solutions obtained here can serve as benchmarks for numerical simulations and for studying complex wave interactions. Overall, this work contributes to the theoretical framework of nonlinear wave dynamics and demonstrates the broad applicability of the -expansion technique across various evolution equations in applied mathematics and engineering.