An Insight into the Solitary Wave Solutions of the 2D-NLSE: Existence Conditions and Parameter Dependence

This study derives and examines a bright solitary-wave solution of the two-dimensional cubic nonlinear Schrödinger equation (2D-NLSE) by combining He’s semi-inverse variational method with the Ritz approach. A complex traveling-wave transformation is used to convert this equation to ordinary differential equation, whereas the decomposition of the real and imaginary components produces an explicit compatibility requirement governing the propagation velocity. A variational functional is created for the reduced equation, and a hyperbolic-secant solution is used as the Ritz trial function. By performing direct substitution, one obtains an independent verification of exactness while simultaneously establishing the amplitude and inverse-width requirements. The analysis indicates that the effective frequency and cubic nonlinearity dictate the maximum amplitude, whereas the effective frequency and directional dispersion determine the pulse width. Furthermore, the simulation presentations for the proposed solutions were displayed using MATLAB software.