Modern Physics Letters B

Nonlinear evolution equations appear in various branches of physics, including fluid dynamics, solid mechanics, quantum mechanics, and other fields. They are essential for describing systems where interactions and nonlinearity play a significant role, providing a more accurate representation of real-world phenomena than linear equations in certain cases. The study of nonlinear evolution equations involves exploring their solutions, stability properties, and the behavior of the systems they describe over time. In this study, we provide plenty of analytical solutions to a very recently proposed water wave model using the modified generalized exponential rational function, modified extended tanh-function, and the $exp(-\phi (\xi ))$-expansion methods. To examine the dynamic characteristics of these results, we displayed three-dimensional (3D), contour, and two-dimensional (2D) visual representations of specific solutions. The outcomes reveal a multitude of novel solutions, emphasizing the robustness and effectiveness of the applied methodologies. It is important to note that all the solutions derived in this study are original and have not been previously documented in the existing literature. These novel solutions hold significant value for researchers in the realms of fluids and plasma physics, providing insights into the dynamics of nonlinear waves within various physical systems. Furthermore, this research contributes to a deeper understanding of the nature of nonlinear waves prevalent in seas and oceans, offering valuable knowledge for the broader study of such phenomena.

This paper presents the effects of various properties on nanofluid flows and heat transfer over a permeable stretching sheet of variable thickness in the presence of a transverse magnetic field. Mathematically, the leading coupled partial differential equations are transformed into a self-similar system of ordinary differential equations through similarity variables, which are solved thereafter using Keller-box and Haar’s wavelet methods. Moreover, the impacts of various flow parameters involved in the physical problem are discussed thoroughly via tables and graphs. As findings, the analysis discloses that the nanofluid flow is significantly influenced by the physical parameters. Dynamically, the nanofluid flow is accelerated prominently with the strengthening in the injection process and decelerated in other situations. Furthermore, the obtained results are compared successfully with the earlier published findings.

In this study, a thermomechanical rigid-flexible coupling vibration model of the rotating pre-twisted porous functionally graded (PP-FG) thick microplate in a thermal environment is established based on the third-order shear deformation theory (TSDT) and modified couple stress theory (MCST). Three thermal distributions are considered. The effects of temperature and porosity on the equivalent material parameters are accounted for in the modified Voigt rule of mixture. The governing equations of motion are derived using the Euler–Lagrange equation and numerically solved through the complex modal analysis method and the Chebyshev–Ritz method. After validating the convergence and accuracy of the proposed model, the effects of temperature, material length scale parameter (MLSP), rotational speed, porosity index, gradient index, presetting angle, and pre-twist angle on the vibration behavior of microplates were examined. The key findings of the study are as follows: (1) The effects of rotational speed on in-plane and out-of-plane frequencies are opposite. Temperature elevation weakens the size effect and centrifugal stiffening effect on the frequencies. (2) The effects of the porosity index on the frequencies are the opposite when the gradient index exceeds a specific critical value. (3) The effects of the presetting angle on the frequencies are periodic and symmetrical at about 0. The frequencies reach an extreme value when the pre-twist angle is approximately 2$\pi$/3 for the cantilever microplate. The proposed model is more sophisticated and comprehensive than others reported in the literature. It offers a more thorough analysis and insight into the behavior and performance of micro-electro-mechanical systems (MEMS) and micro air vehicles (MAVs), particularly when operating in challenging conditions.

Of current interest, there have recently appeared a series of the shallow-water papers in Mod. Phys. Lett. B. Illuminated by those papers and to make the story more complete, for the nonlinear long waves in the shallow water, this paper is scheduled to investigate a (2+1)-dimensional generalized Broer-Kaup system. As for the wave height and wave horizontal velocity, we employ symbolic computation, with the view of constructing out two groups of the similarity reductions.

In this paper, we study Modulation Instability (MI) and its correlated gain spectrum with Parity-Time ($\mathcal{𝒫}\mathcal{𝒯}$)-symmetry. The cubic-quintic nonlinearities in the Bragg grating structure produce ultrashort pulses. The MI evaluation started with a linear stability approach, and we investigated the effects of various system functions regarding the instability gain spectra at the top and bottom sides of the Photonic BandGap (PBG), in addition to the anomalous and normal dispersion domains. The interaction of cubic and quintic (focusing and de-focusing) nonlinearity is highlighted, resulting in a new type of MI band. Due to the consequences of quintic nonlinearity, an additional MI band appears for the three dynamics associated with the gain/loss function for the edges of the bottom PBG. After enforcing the $\mathcal{𝒫}\mathcal{𝒯}$-symmetry for the anomalous dispersion system, the dent transformed into a split under the influence of the power in the de-focusing quintic effect. Overall, MI gain and bandwidths across the entire MI gain spectrum are usually increasing. As an outcome, we are confident that these studies will aid in the generation of gap solitons in $\mathcal{𝒫}\mathcal{𝒯}$-symmetry regimes.

The high nickel ternary LiNi${}_{0.8}$Co${}_{0.1}$Mn${}_{0.1}$O₂ (NCM811) cathode material has attracted much attention owing to its advantages of high capacity and low price. However, NCM811 suffers from surface side reactions and cation mixing, which results in an unstable crystal structure and lower Coulomb efficiency and capacity in lithium ion batteries. In this work, Mo-doped cathode material NCM811 is effectively synthesized by high-temperature solidification approach. The characterization results show that the doped NCM811 can form a coating layer on the surface, preventing electrolyte side reactions with the electrode. As the cathode for lithium ion batteries, the Mo-doped NCM811 electrode shows an initial discharge capacity of 185.21mAh/g and obtains 156.33mAh/g with a capacity retention of 84.5% after 100 cycles at 1C. This study provides a simple and reliable method of fabricating high-performance NCM811 cathode materials.

This study seeks to explore the integrable dynamics of induced curves through the utilization of the complex-coupled Kuralay system. The importance of the coupled complex Kuralay equation lies in its role as a fundamental model that contributes to the understanding of intricate physical and mathematical concepts, making it a valuable tool in scientific research and applications. The soliton solutions originating from the Kuralay equations are believed to encapsulate cutting-edge research in various important domains such as optical fibers, nonlinear optics, and ferromagnetic materials. Analytical techniques are employed to derive traveling wave solutions for this model, given that the Cauchy problem cannot be resolved using the inverse scattering transform. In the quest for solitary wave solutions, the extended modified auxiliary equation mapping (EMAEM) method is employed. We derive several novel families of precise traveling wave solutions, encompassing trigonometric, hyperbolic, and exponential forms. Moreover, the planar dynamical system of the concerned equation is created, all probable phase portraits are given, and sensitive inspection is applied to check the sensitivity of the considered equation. Furthermore, after adding a perturbed term, chaotic and quasi-periodic behaviors have been observed for different values of parameters, and multistability is reported at the end. Numerical simulations of the solutions are incorporated alongside the analytical results to enhance comprehension of the dynamic characteristics of the solutions obtained. This study’s outcomes can offer valuable insights for addressing other nonlinear partial differential equations (NLPDEs). The soliton solutions obtained in this study offer important insights into the intricate nonlinear equation being examined.

Permanent magnet synchronous motor (PMSM) is a multivariable and highly coupled nonlinear system, which is prone to chaotic behavior during actual operation. In order to suppress the chaotic behavior of the PMSM, this work designs a free-will arbitrary time adaptive controller based on the inverse step derivation, adaptive control theorem and Lyapunov stability theory. Firstly, the corresponding coordination transformations are designed according to the PMSM. Secondly, the bounded problem of the controlled system is analyzed by using the Lyapunov stability theory, and the free-will arbitrary time adaptive controller is designed by backstepping derivation. Finally, numerical simulation verifies that the designed controller quickly stabilizes the system state variables to the output signals and proves that the controller is free-will arbitrary time stable for all closed-loop signals.

Motile cilia are hair-like, tiny structures that originate in different types of biological processes. Yeleswarapu fluid model is approximated as non-Newtonian mucus, which is viscous and slippery fluid with key roles in lubrication, protection, and particle trapping in the respiratory and digestive systems. The properties of Yeleswarapu fluid with heat transfer in ciliated channels are investigated in this study. The fluid flow is characterized as laminar (low Reynold number) and incompressible (constant density) in a two-dimensional complex wavy channel generated via metachronal waves of cilia. A static frame of reference is first transformed into a dynamic frame of reference. Afterward, the system of governing equations is transformed into a non-dimensional form by using scaling factors. The half-width of the channel is substantially smaller than the wavelength of metachronal waves. Hence, the constitutive equations are simplified by the long wavelength hypothesis. The perturbation approach is employed to solve the simplified system of differential equations. This research investigates how different boundary walls and rheology affect fluid flow. Additionally, graphs of the streamlines, velocity field, temperature, heat transfer coefficient, and pressure rise are included.

In this paper, novel soliton solutions to the conformable time fractional Benjamin–Bona–Mahony and seventh-order time fractional Sawada–Kotera–Ito equations are investigated via application of two mathematical methods. These models are reformulated into a fractional order derivative by applying the conformable derivative operator. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic and exponential function solutions. For physical phenomena of concern models, some solutions are plotted in two-dimensional and three-dimensional by assigning the particular values to the parameters under the constrain conditions with the assistance of Mathematica software. Hence, all results obtained by our proposed methods are novel and have not been yet reported in any literature. Moreover, the proposed schemes are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science.

This paper’s goal is to investigate the oscillatory flow of double-diffusive convection in a Voigt fluid. We re-design the basic equations of the channel flow, which initially appear dimensional, in a dimensionless manner using non-dimensional variables. The oscillation technique transforms the governing equations into coupled ordinary differential equations (CODEs). We have derived the analytical expressions for velocity, temperature, and concentration distribution by solving the CODEs using the direct analytical method. The study focuses on how physical factors, like the thermal Grashof number, the solutal Grashof number, the Prandtl number, the Lewis number, and the Voigt fluid parameter, affect different aspects of flow, such as speed, temperature, concentration, rate of heat transfer, and mass transfer. Notably, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate. The significance of double-diffusive oscillatory flow lies in its ability to improve heat and mass transfer rates, as well as its impact on pattern formation and stability, which influences a wide range of applications from engineering design to environmental studies.

Here attention is focused on the (1+1)-dimensional Sawada–Kotera (SK) model that is prominent in mathematical physics and engineering to analyze plasmas and coherent systems for communication. Our techniques offer fresh perspectives on the model’s attributes and structure, deepening our comprehension of the underlying dynamics. First, the SK model is reduced to ordinary differential equations by constructing the Lie symmetries and using the associated transformation. Graphs are used to build and display invariant solutions. This strategy has caused the revelation of novel constant solutions that have not been found in the previous works. We offer new understandings of nature and changes observed during the SK derivation by taking advantage of the Lie symmetries powerful tools. Next, the fluctuating layout of proposed framework is examined from several perspectives such as sensitivity and bifurcation analysis. We examined the bifurcation analysis of planar dynamical system by using bifurcation theory. We also include an external periodic perturbation term that breaks regular patterns in the perturbed dynamical system. Graphical structures are provided to display the invariant solutions. The sensitivity of the SK model is determined to be strong after sensitivity analysis under different initial conditions. These results are fascinating, fresh, and conceptually useful for understanding the suggested framework. In mathematics and the applied sciences, forecasting and learning about new technologies are greatly aided by the dynamic aspect of system processing.