Bright, dark, and periodic soliton solutions for the (2+1)-dimensional nonlinear Schrödinger equation with fourth-order nonlinearity and dispersion

This paper introduces a novel model proposed by Wazwaz et al. in 2023, in the nonlinear optics literature. This contributes to advancing optical devices and technologies, particularly in telecommunications and laser systems. The characteristics of bright, dark, and periodic soliton solutions for the (2+1)-dimensional nonlinear Schrödinger equation with fourth-order nonlinearity and dispersion are explored in this paper. The relevance of these solutions lies in the study of nonlinear waves propagating in an inhomogeneous optical fiber. The soliton solutions are obtained through the implementation of three analytical methods: the Kudryashov method, the Bernoulli Sub-ODE method, and the Extended Direct Algebraic method. The bright, dark, and periodic soliton solutions are constructed by utilizing bilinear forms. Furthermore, the impact of variable coefficients on the structures of these solitons is analyzed. Graphical illustrations depict the propagation of bright, dark, and periodic solitons.