Bright and dark optical modulated soliton solutions for the fourth-order (2+1)-dimensional Schrödinger equation with higher-order odd and even terms

This work addresses a (2+1)-dimensional nonlinear Schrödinger (NLS) equation (NLSE) with fourth-order nonlinearity and dispersion. Some different solutions in the form of bright and dark optical modulated solitons (OMSs) to the current problem are derived using different approaches. Moreover, based on some certain conditions for the related parameters, some, bright, dark, periodic, exponential, and singular modulated solutions are obtained. The derived solutions can be helpful in understanding the bright and dark OMSs features of identical models in optical fields, fluid mechanics, and plasmas.