Akademik Veri Yönetim Sistemi
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, sa.26, ss.1-58, 2026 (SCI-Expanded, Scopus)
KABUL EDİLDİ
In this paper, the sixth-order Benney-Luke equation as a nonlinear partial differential equation that deter19 mines how nonlinear waves travel through analyzing wave tension in physical systems and studying the 20 stress of water surface is studied. The method employs Hirota’s bilinear form to construct diverse solu21 tion models, including the multi waves, breather waves, Ma-breather, Kuznetsov-Ma-breather, periodic 22 cross-kink solutions. These solutions offer critical insights into the impact of behaviours on nonlinear 23 wave dynamics, particularly in the stress of water surface. Also, in this study, some standard, compat24 ible, and useful wave solutions with a high score of accuracy and applicability, designated in terms of 25 hyperbolic, trigonometric, and rational functions of the stated models using the generalized tan(φ/2)- 26 expansion approach are established. The model is adapted to univariate wave equations through wave 27 transformation erstwhile to investigation. To enhance visualization, we use Maple software to plot three28 dimensional, two-dimensional, and density graphs, illustrating the intricate effects of solitons and other 29 kinds of solutions on the obtained solutions. This work contributes to the understanding of soliton 30 dynamics in higher-dimensional nonlinear systems and their relevance in practical applications. The ob31 tained solutions are compared with the exact or existing numerical results in the literature to verify the 32 applicability, efficiency and accuracy of the method. The acquired results reveal the efficiency and sim33 plicity of the suggested techniques which are more conscientious to solve higher dimensional nonlinear 34 ordinary as well as partial differential equations.