In this article, we utilize the G′/G2-expansion method and the Jacobi elliptic equation method to analytically solve the (2 + 1)-dimensional integro-differential Jaulent–Miodek equation for exact solutions. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrödinger potentials (Jaulent and Miodek, 1976; Jaulent, 1976). The equation is converted into a fourth order partial differential equation using a transformation. After applying a traveling wave transformation to the resulting partial differential equation, we obtain an ordinary differential equation which is the main equation to which the both schemes are applied. As a first step, the two methods give us distinguish systems of algebraic equations. The first method provides exact traveling wave solutions including the logarithmic function solutions of trigonometric functions, hyperbolic functions, and polynomial functions. The second approach provides the Jacobi elliptic function solutions depending upon their modulus values. Some of the obtained solutions are graphically characterized by the distinct physical structures such as singular periodic traveling wave solutions and peakons. A comparison between our results and the ones obtained from the previous literature is given. Obtaining the exact solutions of the equation shows the simplicity, efficiency, and reliability of the used methods, which can be applied to other nonlinear partial differential equations taking place in mathematical physics.

The Benney-Luke equation has contributed to studying the propagation of the water wave surfaces. This paper illustrates the (G’/G,1/G)-method to obtain the solutions of the Benney-Luke equation and an extension of the Benney-Luke equation. The new types of solutions are also constructed to gather the performance and visualization in three dimensions for observing the behaviors. The solutions are found in the expressions of hyperbolic functions giving the general performance by selecting arbitrary constants.

In the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

The Sharma–Tasso–Olver (STO) equation is a nonlinear, double-dispersive, partial differential equation that is physically important because it provides insights into the behavior of nonlinear waves and solitons in various physical areas, including fluid dynamics, optical fibers, and plasma physics. In this paper, the STO equation is generalized to a fractional equation by using Atangana (or Atangana–Baleanu) fractional space and time beta-derivatives since they have been found to be useful as a model for a variety of traveling-wave phenomena. Exact solutions are obtained for the integer-order and fractional-order equations by using the Sardar subequation method and an appropriate traveling-wave transformation. The exact solutions are obtained in terms of generalized trigonometric and hyperbolic functions. The exact solutions are derived for the integer-order STO and for a range of values of fractional orders. Numerical solutions are also obtained for a range of parameter values for both the fractional and integer orders to show some of the types of solutions that can occur. As examples, the solutions are obtained showing the physical behavior, such as the solitary wave solutions of the singular kink-type and periodic wave solutions. The results show that the Sardar subequation method provides a straightforward and efficient method for deriving new exact solutions for fractional nonlinear partial differential equations of the STO type.

In this paper, we demonstrate the effectiveness of an entomopathogenic fungus, namely, Metarhizium to reduce environmental problems arising from the use of insecticides. Metarhizium species used in the article include M. anisopliae sensu stricto, M. anisopliae sensu lato, and M. pingshaense. The efficacy of them in controlling the spread of the brown planthopper (BPH) collected from three different regions of Thailand, including Phetchabun Province, Buri Ram Province and Phatthalung Province, was analyzed. Using actual data representing the daily mortality of BPH, we estimated the corrected mortality. In addition, we studied four candidate BPH survival functions, namely the Gompertz model, the Weibull model, the sigmoid model, and the log-logistic model, in order to achieve the best model fitting to the experimental data. As a result, most of the data was best fitted by the log-logistic model. We also used the susceptible infected model to determine the transmission rate from susceptible BPH to infected BPH. Finally, the lethal time formulas and the estimated values of time required for 50% and 90% mortality were obtained using the log-logistic survival and SI models. From the results, the obtained lethal times for both models have the same trends. It is worth noticing that the M. anisopliae sensu lato fungus gave the most effective results in destroying BPH based on the percentages of corrected mortality, lethal time values and transmission rate.

This article evaluates the effectiveness of two Metarhizium neoanisopliae strains (ARSEF7487, BCC4849) and five Metarhizium sulphureum strains (BCC12791, BCC18130, BCC36572, BCC36592, BCC39045) against the brown planthopper (BPH), a major rice pest. A survival analysis was conducted using four parametric survival functions: Weibull, log-normal, gamma, and log-logistic, with the best-fitting models determined by the Akaike and Bayesian information criteria. Additionally, the goodness-of-fit was tested using the Kolmogorov–Smirnov, Anderson–Darling, and Cramer–von Mises tests. Results indicated that the log-normal distribution provided the best overall fit for the data. Among the tested strains, Metarhizium neoanisopliae strain BCC4849 showed the highest mortality rate of 79.99\(\%\), followed closely by Metarhizium sulphureum strain BCC36572 with 67.10\(\%\) mortality. The log-rank test confirmed that these two strains did not significantly differ in efficacy under the same experimental conditions. These findings suggest that Metarhizium neoanisopliae strain BCC4849, along with Metarhizium sulphureum strain BCC36572, could serve as highly effective biological control agents for managing BPH populations, offering a sustainable alternative to chemical insecticides.