Modulational instability and pure-quartic solitary waves in the presence of the Bohm potential

Abstract Over the last few decades, the investigation of mathematical models related to Earth systems has garnered significant research attention. In the present paper, the propagation of pure-quartic solitary waves (PQSWs) within an optical medium involving linear and nonlinear effects is formally analyzed. It is shown that such a physical system, which benefits from fourth-order dispersion/diffraction, Kerr nonlinearity, weak nonlocality, and the Bohm potential, consists of a wide range of continuous periodic and solitary waves. It has been observed that all physical effects play crucial roles in the dynamics of pure-quartic solitary waves. A variety of case studies have been carried out to examine the influence of linear and nonlinear effects on the behavior of localized wave structures. Through the linear stability analysis, the modulational instability (MI) of the governing equation is examined, and the impact of such effects on the MI spectrum is assessed. The findings offer extensive and significant insights regarding the current optical system with such linear and nonlinear effects.