Optical dark, singular and bright soliton solutions with dual-mode fourth-order nonlinear Schrödinger equation involving different nonlinearities

This research article investigates the dynamic characteristics of solitary waves within a medium exhibiting weak nonlinearity in dual-mode. Firstly, the three models are converted to dual-mode. The primary focus is to investigate the behavior of solitary waves in a system described by a fourth-order nonlinear Schrodinger (NLS) equation, which incorporates Kerr nonlinearity, weak nonlocality, parabolic law nonlinearity and diffraction. By employing ansatz methods, the study successfully derives various localized waveforms, including bright, dark and singular solitons, based on the governing model. The examination extends to investigating the influence of nonlocality and power coefficients on dynamics of bright, dark and singular solitons. The findings presented in this article represent a crucial advancement in understanding the generation of solitary waves in nonlinear media. As the examined model finds application in various fields such as plasma physics, Bose-Einstein condensates and others, these findings not only enhance our theoretical understanding but also pave the way for potential practical applications and the advancement of innovative technologies.