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This work examines the (2+1)-dimensional Boiti-Leon-Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti-Leon-Pempinelli equation by applying the Sardar sub-equation technique. This method is shown to be a reliable and practical tool for solving nonlinear wave equations. Furthermore, different types of solitary wave solutions are constructed: w-shaped, breather waved, chirped, dark, bright, kink, unique, periodic, and more. The results obtained with the variable coefficient Boiti-Leon-Pempinelli equation are stable and different from previous methods. As compared to their constant-coefficient counterparts, the variable-coefficient models are more general here. In the current work, the problem is solved using the Sardar Sub-problem Technique to produce distinct soliton solutions with parameters. Plotting these graphs of the solutions will help you better comprehend the model. The outcomes demonstrate how well the method works to solve nonlinear partial differential equations, which are common in mathematical physics.With the help of this method, we may examine a variety of solutions from significant physical perspectives., (© 2024. The Author(s).)

In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties. The stochastic backward Euler (SBE) and stochastic Implicit finite difference (SIFD) schemes are designed for the computational results. In the mean square sense, both schemes are consistent with the underlying model and schemes are von Neumann stable. The underlying model has various equilibria points and all these points are successfully gained by the SIFD scheme. The SIFD scheme showed positive and convergent behavior for the given values of the parameter. As the underlying model is a population model and its solution can attain minimum value zero, so a solution that can attain value less than zero is not biologically possible. So, the numerical solution obtained by the stochastic backward Euler is negative and divergent solution and it is not a biological phenomenon that is useless in such dynamical systems. The graphical behaviors of the system show that external nutrient supply is the important factor that controls the dynamics of the given model. The three-dimensional results are drawn for the various choices of the parameters., (© 2024. The Author(s).)

In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction-diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reaction†"diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system's diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants., (© 2023. The Author(s).)

Warburg effect is an emerging hallmark of cancer cells with pyruvate kinase M2 (PKM2) as its key regulator. Curcumin is an extensively-studied anti-cancer compound, however, its role in affecting cancer metabolism remains poorly understood. Herein, we show that curcumin inhibits glucose uptake and lactate production (Warburg effect) in a variety of cancer cell lines by down-regulating PKM2 expression, via inhibition of mTOR-HIF1α axis. Stable PKM2 silencing revealed that PKM2 is required for Warburg effect and proliferation of cancer cells. PKM2 over-expression abrogated the effects of curcumin, demonstrating that inhibition of Warburg effect by curcumin is PKM2-mediated. High PKM2 expression correlated strongly with poor overall survival in cancer, suggesting the requirement of PKM2 in cancer progression. The study unravels novel PKM2-mediated inhibitory effect of curcumin on metabolic capacities of cancer cells. To the best of our knowledge, this is the first study linking curcumin with PKM2-driven cancer glycolysis, thus, providing new perspectives into the mechanism of its anticancer activity.