Abundant new soliton solutions to the Arshed–Biswas equation via two novel integrating schemes

This paper explores analytical solutions to the Biswas–Arshed equation, a key mathematical model describing soliton propagation in optical fibers. Understanding and solving this equation provide insights into signal stability, dispersion management, and overall improvements in fiber-optic communication technology. To achieve this, we first decompose the equation into real and imaginary components, deriving a system of nonlinear differential equations. We then employ the Kumar–Malik method and the polynomial expansion method — two powerful analytical techniques applied for the first time to this equation — to construct exact solutions. These methods yield soliton solutions in Jacobi elliptic, exponential, hyperbolic, and trigonometric forms, with numerical simulations visualized through 3D, contour, density, and 2D plots. The significance of these findings extends beyond theoretical mathematics. Optical soliton solutions derived from this study can contribute to the development of more efficient optical fiber networks, enhanced data transmission techniques, and improved nonlinear wave applications in photonics. By leveraging advanced analytical methods, this research provides new solution sets that could aid in optimizing real-world optical systems, potentially influencing future advancements in telecommunication infrastructure, high-speed internet technologies, and laser pulse dynamics.