本研究考察了伪抛物非线性Oskolkov-Benjamin-Bona-Mahony-Burgers(OBBMB)方程,广泛适用于光纤等领域,土壤固结,热力学,非线性网络,波传播,和岩石不连续性中的流体流动。波变换和广义Kudryashov方法用于推导常微分方程(ODE)并获得解析解,包括明亮,反扭结,黑暗,和扭结孤子。ODE的系统,然后通过考虑参数变化的平衡点的分叉分析进行检查。此外,为了深入了解一些外力的影响,已经采用了扰动理论。为此,各种混沌检测技术,例如poincaré图,时间序列剖面,3D相位肖像,多稳定性调查,实现了lyapounov指数和分岔图,以识别扰动动力学模型的准周期和混沌运动。这些技术可以分析扰动的动力学系统如何混乱并偏离常规模式。此外,观察到基础模型是相当敏感的,因为即使初始条件略有变化,它也会发生巨大变化。这些发现很有趣,在数学和物理模型中新颖且理论上有用。这些为科学家和研究人员提供了一种有价值的机制,以研究这些扰动如何影响系统的行为以及它偏离未扰动情况的程度。
This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink
solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system\'s behavior and the extent to which it deviates from the unperturbed case.