Influence of fourth-order dispersion on the formation of localized states in systems with inhomogeneous defocusing nonlinearity

Abstract

The formation and stability of localized structures in nonlinear dispersive media remain subjects of intense research, particularly in the context of higher-order effects. In this work, we investigate the role of fourth-order dispersion (FOD) in the emergence of localized states in systems governed by inhomogeneous defocusing nonlinearities. While defocusing nonlinearities typically act to suppress localization, recent studies have demonstrated that spatially varying nonlinearity profiles can counteract dispersion and lead to the formation of robust localized modes. By incorporating a fourth-order dispersive term into the governing nonlinear Schrödinger-type equation, we analyze the interplay between nonlinearity modulation and higher-order dispersion. Our results reveal that FOD not only modifies the spatial profile and stability of localized solutions but also enables the existence of novel bound states that are otherwise inaccessible in the absence of such higher-order effects. These findings provide new insights into the design of advanced photonic and matter-wave systems, where engineered dispersion and nonlinearity landscapes can be exploited for controlled localization phenomena.