New novel solitonic-like solutions describing two dimensional Schrödinger equation with source term

In this study, we used the Riccati–Bernoulli technique to generate new solitary structures for the model of the nonlinear two-dimensional Schrödinger equation (NTDNLSE) with a source term. These structures included rational, periodic, solitary, explosive, dissipative, and blow-up solitons. To demonstrate the shape of the obtained solutions for suitable free parameter values, a few 2D and 3D charts are displayed. The dynamical and phase portrait behaviors with the aid of model parameters controlled the type of obtained NTDNLSE solitary solutions. The properties of NTDNLSE structure solutions that depend on the Kerr, drift, and dispersion have been investigated. Many fluid and space plasma applications depend on the dynamical behaviors of these solutions. The results show how straightforward and quick this method is for constructing elaborate nonlinear wave patterns and rich exact solutions to nonlinear equations in mathematical physics.