A Fourth-Order Nonlinear Schrödinger Equation Involving Power Law and Weak Nonlocality: Its Solitary Waves and Modulational Instability Analysis

The present paper examines the dynamical features of solitary waves in a weakly nonlinear medium. More precisely, the propagation of solitary waves in a system is modeled by a fourth-order nonlinear Schrödinger equation involving diffraction, power law nonlinearity, and weak nonlocality. Several localized waves classified as bright and dark solitons to the governing model are derived using ansatz methods. It is shown how power and nonlocality coefficients affect the dynamics of bright and dark solitons. Furthermore, the modulational instability of continuous waves in the presence of such different effects is studied. The results of the current paper represent a significant advancement in exploring the propagation of solitary waves in a nonlinear medium.