Necessary conditions for convex-periodic, elliptic-periodic, inclined-periodic, and rogue wave-solutions to exist for the multi-dispersions Schrodinger equation

In this study, we revisit the modified Schrödinger equation, which incorporates multiple dispersion terms, including linear, nonlinear, and random dispersion. We establish the essential constraints on the model’s parameters to ensure the presence of complex-valued solutions. Subsequently, we employ effective and explicit techniques such as the extended tanh-coth expansion, rational sine-cosine functions, and rational sinh-cosh functions to derive innovative types of periodic solutions for the proposed model. These solutions demonstrate unique physical properties applicable to various complex media, such as surface water waves, optical fiber pulses, and plasma waves.