Akademik Veri Yönetim Sistemi
International Journal of Theoretical Physics, cilt.65, sa.1, 2026 (SCI-Expanded, Scopus)
In this study, we aim to derive exact analytical solutions, specifically bright soliton and singular solutions, for the pure-cubic nonlinear Schrödinger equation with third-order dispersion, incorporating cubic–quintic–septic nonlinearities, and to investigate its dynamic behavior through modulation instability analysis. This model, characterized by the dominance of third-order dispersion and the absence of the standard group-velocity dispersion term, accurately reflects realistic wave evolution in ultrafast optics and supercontinuum generation. The equation was analyzed using the new Kudryashov’s scheme, which is highly effective for solving high-order nonlinear Schrödinger-type equations. To complement this, a detailed modulation instability analysis was performed. As a result, bright soliton and singular solutions were successfully obtained. Furthermore, the conditions under which the model exhibits modulation instability were precisely identified. The findings were illustrated through 2D and 3D graphical representations. The primary novelty of this work lies in the successful application of the new Kudryashov method and the subsequent detailed modulation instability analysis to this particular, highly-nonlinear form of the Schrödinger equation. The derived analytical solutions serve as crucial benchmark data for future studies involving external perturbations.