ZI-GE WU, Kang‐Le Wang
The Schrödinger equation occupies a significant place in quantum mechanics, and the wave functions as its solutions provide a comprehensive understanding of a quantum system. In this paper, the perturbed fractional nonlinear Schrödinger equation (PFNSE) is investigated by utilizing the modified fractional extended direct algebraic method and the tanh function method. Some new solitary wave solutions are triumphantly derived. Finally, the dynamic behaviors of the obtained solitary wave solutions are elaborated by plotting the three-dimensional and two-dimensional graphs with proper parameters. This study’s results can be beneficial for gaining an in-depth comprehension of the nonlinear dynamic characteristics of a system and demonstrating the effectiveness of the current methods, thereby making a significant contribution to high-dimensional nonlinear wave fields. We anticipate that our analysis will benefit a substantial number of scientific models and other related problems.