This article studies the nonlinear wave dynamics of the recently introduced integrable combined Kairat-II-X (K-II-X) equation, which combines dynamical features of the Kairat-II and Kairat-X models. The considered model possesses relevance in nonline...
Based on the hydrodynamic description, the dynamics of nonlinear cylindrical waves in an isentropic plasma are investigated. The problem is considered in an electrostatic formulation for a two-dimensional plasma medium where ions form a stationary ba...
The nonlinear dynamic response of an aquaculture cage array caused by wave-frequency and low-frequency excitations coupled with the nonlinearity of the mooring and the netting system is a complicated problem. So far, this problem still has not been c...
The air separation process is an important industrial process for the production of high-purity nitrogen and oxygen, representing the level of technological development in a country’s chemical industry. It has high energy consumption but very l...
This study examines the mechanism of nonlinear supratransmission (NST), which involves the transfer of disturbance to discrete media at frequencies not supported by the structure. We considered a model crystal with A3B stoichiometry. The investigatio...
The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surfac...
This study examines a nonlinear partial differential equation, namely the (3+1)-dimensional Boussinesq-type equation. To explore this model, three versatile analytical approaches are applied: the Exp-function method, the Kudryashov method, and the Ri...
In this paper, the nonlinear wave dynamics of the (3+1)-dimensional P-type model are investigated using a symbolic neural-network-based hybrid technique. The model is considered in the context of nonlinear wave propagation, which is of practical impo...
This study employs the modified extended direct algebraic method (MEDAM) to investigate the generalized nonlinear fractional
In this study, a detailed analytical-numerical study of the complex modified Korteweg–De Vries (mKdV) model with truncated M-fractional derivative is carried out to investigate the effects of the fractional order on nonlinear wave propagation....
In this research, we investigate the phenomenon of multistability and complex dynamic behaviors in plasma waves by utilizing advanced mathematical techniques. We examine how fractional-order derivatives influence plasma wave stability by applying the...
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 differ...
This study investigates the dynamics of optical solitons for the variable-coefficient coupled higher-order nonlinear Schrödinger equation (VCHNLSE) enriched with
This report bridges fundamental ideas from introductory calculus to advanced concepts in quantum mechanics and nonlinear dynamics. Beginning with the behavior of second derivatives in oscillatory and exponential functions, it introduces the Airy equa...
The central objective of this study is to develop some different wave solutions and perform a qualitative analysis on the nonlinear dynamics of the time-fractional chiral nonlinear Schrodinger’s equation (NLSE) in the conformable sense. Combine...
The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonl...
Optical rogue waves are a nonlinear phenomenon that offers a unique opportunity to gain fundamental insights into wave interaction and behavior, and the evolution of complex systems. Optical systems serve as a suitable testbed for the well-controlled...
Wave energy converters (WECs) usually require reactive power for increased levels of energy conversion, resulting in the need for more complex power take-off (PTO) units, compared to WECs that do not require reactive power. A WEC without reactive pow...
Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assump...
Fishing boats anchored away from the wharf or revetment are typically in side-by-side configurations due to their small size. Expanding on previous physical model tests investigating regular wave interactions with multi-boat and bow-and-stern-anchore...
A novel modified generalized Riccati equation mapping neural network-based approach is the basic theme of this study by exploring the nonlinear dynamical characteristics of the the strain wave model’s soliton solutions, which govern wave propag...
This paper investigates the possibilities of complex nonlinear dynamic signal generation using a simple photorefractive two-wave mixing system without any feedback using numerical simulations. The novel idea is to apply a sinusoidal electric field to...
Dynamic Wave Energy Converter (WEC) models utilize a wide variety of fundamental hydrodynamic theories. When incorporating novel hydrodynamic theories into numerical models, there are distinct impacts on WEC rigid body motions, cable dynamics, and fi...
In this paper, we present numerical modelling for the investigation of dynamic responses of a floating offshore wind turbine subject to focused waves. The modelling was carried out using a Computational Fluid Dynamics (CFD) tool. We started with the...
Due to the rapid development of theoretical and computational techniques in the recent years, the role of nonlinearity in dynamical systems has attracted increasing interest and has been intensely investigated. A study of nonlinear waves in shallow w...
In this study, the nonlinear dynamics of nanoparticle concentration in a colloidal suspension (nanofluid) were theoretically studied under the action of a light field with constant intensity by considering concentration convection. The heat and nanop...
Freak waves have caused numerous accidents resulting in the collapse of ship structures due to structural plasticity, buckling, and instability, leading to the loss of life and property. Consequently, there is a growing academic interest in understan...
This paper presents a comprehensive method for analyzing prestressed concrete bridges subjected to multiple concurrent dynamic loads, incorporating soil–structure interaction (SSI) and seismic wave propagation effects. The study develops a comp...
Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardwar...
Generalized frosts have a significant impact on the Pampa Húmeda of Argentina, particularly those without persistence (0DP), defined as events that do not last more than one day, and are the most frequent generalized frosts. This study investi...
While billiard systems of various shapes have been used as paradigmatic model systems in the fields of nonlinear dynamics and quantum chaos, few studies have investigated anisotropic billiards. Motivated by the tremendous advances in using and contro...
The Edinburgh Duck is one of the highly-efficient wave energy converters (WECs). Compared to the spine-connected Duck configuration, the solo Duck will be able to use the point absorber effect to enhance its power capture performance. In this paper,...
This paper proposes a super-twisting sliding-mode control (STSMC) strategy to enhance the efficiency and stability of a heaving point absorber wave energy converter (PAWEC) system equipped with a permanent magnet synchronous generator (PMSG). In part...
We present a review on the application of the mathematical models for research on social processes, social structures, and actors in social systems. The scope of the review is not restricted to the classical applications of mathematics such as theory...
In this study, we discuss the dynamical behaviors and extract new interesting wave soliton solutions of the two significant well-known nonlinear partial differential equations (NPDEs), namely, the Korteweg–de Vries equation (KdVE) and the Jaule...
This study applies the Conformable Laplace Adomian Decomposition Method (CLADM) to solve generalized time-fractional Korteweg–de Vries (KdV) models, including seventh- and fifth-order models. CLADM combines the conformable fractional derivative...
The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-e...
This work addresses the significant issue of plasma waves interacting with non-linear dynamical systems in both perturbed and unperturbed states, as modeled by the generalized Whitham–Broer–Kaup–Boussinesq–Kupershmidt (WBK-BK)...
The baryonic mass–velocity relation provides an important test of different galaxy dynamics models such as Lambda–cold dark matter (
To describe the meaning of functionality in a universe before life evolved, existing etiological and systemic accounts of function are evaluated. Since the theory of function is only applicable in context with living beings and artifacts used by livi...
We consider a two-component linearly coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in b...
A frequency comb generator (FCG) based on dual-cavity Brillouin random fiber lasing oscillation in the 1.5 μm telecon spectral window is established and experimentally demonstrated. In the half-open main cavity of the dual cavity, the stimulated B...
We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian
The fourth-order nonlinear Boussinesq water wave equation, which describes the propagation of long waves in the intertidal zone, is investigated in this study. The exact wave patterns of the equation were computed using the
In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear par...
This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned...
Stochastically forced nonlinear wave systems are commonly associated with complex dynamical behavior, although little is known about the general interaction of nonlinear dispersion, irrational forcing frequencies, and multiplicative noise. To fill th...
The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obt...
The soliton waves’ physical behavior on the pseudo spherical surfaces is studied through the analytical solutions of the nonlinear (1+1)–dimensional Kaup–Kupershmidt
The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks...
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