Sep 2026· Zeitschrift für Naturforschung A· 0 citations· 65 references
Abstract
Abstract The time-fractional Boussinesq equation helps in the modeling of various physical phenomena, such as shallow water waves and coastal engineering, to model tsunamis. This paper investigates the time-fractional Boussinesq equation, after introducing memory effect through the time fractional parameter β ∈ (0, 1]. Exact solutions are derived with the help of the (G′/G, 1/G)-expansion method, yielding the solitons for different cases, i.e., hyperbolic, trigonometric, and rational. The influence of the fractional order on solution profiles is examined through three-dimensional plots in terms of amplitude modulation, wave localization, and propagation dynamics. Furthermore, bifurcation analysis is performed to identify stability transitions using the formation of a Hamiltonian system. Along with that, the chaotic behavior is further examined using the three-dimensional plots, and Poincaré plots are employed to identify stability transitions and complex dynamical transitions. For validating the results, Lyapunov exponent and sensitivity analysis have been carried out.
This article presents a comprehensive analytical and dynamical investigation of the (4+1)-dimensional variable-coefficient generalized Kadomtsev Petviashvili equation (vc-gKP). Exact analytical solutions are constructed using the modified Khater method, constructing a diverse class of localized and propagating wave str...
Muhammad Iqbal, Muhammad Aziz ur Rehman, Z. Shah· Punjab University journal of...· 0 citations
The Yajima–Oikawa equations describes the resonant interaction between ion sound waves and Langmuir waves in plasma. Despite its importance, the detailed dynamical behavior of this model has not been comprehensively explored. In this work, we present a unified analytical and dynamical framework that combines exact so...
H. H. Abdulkareem, H. Ismael, S. Ahmed et al.· Scientific Reports· 0 citations
In this paper, the nonlinear Nurshuak–Tolkunay–Myrkakulov (NTM-III) equation is analyzed using the methods of dynamical systems theory and exact solution techniques. The NTM-III model is reduced to a second-order nonlinear ordinary differential equation by using appropriate reductions, then written as a planar Hamilton...
Abdulrahman B. M. Alzahrani· Symmetry· 0 citations
In this study, an analytical and dynamical study of the classical Kolmogorov–Petrovsky– Piskunov (KPP) equation is carried out by means of the improved generalized Riccati equation mapping (IGREM) method. An appropriate traveling-wave transformation is used to reduce the governing equation and several families of exact...
Julien Moussa H. Barakat, Raymond Ghandour, Zaher Al Al Barakeh· Computation· 0 citations
In this paper, we focus on the dynamical analysis and soliton solutions of the Vakhnenko–Parkes (VP) equation. Initially, an appropriate transformation is applied to the VP equation to reduce it to a nonlinear ordinary differential equation. Subsequently, a Galilean transformation is employed to obtain the correspondin...
Beenish, Muhammad Ishfaq Khan, Asad Ullah Khan et al.· Boundary Value Problems· 0 citations
