Soliton solutions of cubic quintic septimal nonlinear Schrödinger wave equation with conformable derivative by two distinct algorithms

Abstract This paper investigates the cubic-quintic-septimal nonlinear Schrödinger wave equation with a conformable derivative, which governs the evolution of light beams in a weak nonlocal medium. The analysis utilizes the Kudryashov method and the enhanced modified tanh expansion method. By utilizing these analytical integration schemes, various optical wave solutions are derived within the present conformable model. The paper demonstrates the significance of these optical soliton solutions by illustrating different soliton solutions, including kink-type, bell-shaped, singular, dark, and wave soliton solutions, depicted via contour, three-dimensional, and two-dimensional representations. Moreover, it is crucial to emphasize the importance of analyzing the cubic-quintic-septimal nonlinear Schrödinger wave equation, which finds utility across a spectrum of fields including optics, quantum mechanics, and the study of nonlinear wave propagation. Moving forward, these approaches hold promise for investigating diverse sets of differential equations within multiple domains of applied sciences. This governing equation also has numerous applications in nonlinear optics, such as describing the propagation of laser beams through materials with nonlinear optical properties. The inclusion of these nonlinearities illustrates the interaction and behavior of light beams in weakly non-local media.