A highly effective analytical approach to innovate the novel closed form soliton solutions of the Kadomtsev–Petviashivili equations with applications

Exploring Novel Soliton Solutions to the Time-Fractional Coupled Drinfel’d–Sokolov–Wilson Equation in Industrial Engineering Using Two Efficient Techniques

“…Given the substantial interest and importance placed on obtaining exact solutions for NLEs, numerous researchers have endeavored to employ a diverse array of mathematical techniques to achieve this objective. These techniques encompass a wide spectrum of methodologies, including the modified simple equation method [12], the generalized (G ′ /G)-expansion technique [13], the ( G ′ G ′ +G+A ) technique [14], the Hirota bilinear method [15], the Riccati equation technique [16], the Lie group approach [17], the extended Jacobi elliptic function approach [18], the exp {−φ(ξ)} method [19], the functional variable technique [20], the multiple exp-function technique [21], the new auxiliary equation technique [22], the tanh-function approach [23], the simple equation technique [24], the tanh-coth technique [25], the generalized Kudryshov technique [26], the unified technique [27], and so on.…”

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

“…Optical solitons offer unique benefits, such as stable propagation over long distances and the preservation of pulse shape and integrity. As a result, accurate modeling of soliton dynamics is of paramount importance for advancing and optimizing optical devices and systems tailored for these specific applications [1][2][3][4]. Within the realm of optical fiber communication, the significance of the BME is notable, as it stands as a valuable tool for modeling diverse soliton solutions.…”