<p>This paper presents a comprehensive analytical study of the stability and dynamics of soliton solutions to a higher-dimensional nonlinear Schrödinger equation influenced by time-dependent external potential. Utilizing two complementary approaches, the separation of variables method and a generalized solitary wave ansatz with time-dependent phase and traveling wave coordinates, we systematically derive a wide range of exact solutions, including bright, dark, mixed bright-dark, and singular solitons, as well as periodic waveforms. A key contribution of this work is the introduction of a novel energy-like functional that quantitatively evaluates the stability of bright solitons. By integrating this global energy-based metric with local linear stability analysis, the paper offers a robust framework for assessing the resilience of soliton solutions. The analysis reveals that constant and bounded potentials preserve soliton structure, while linearly increasing potentials cause spatial broadening without compromising stability. These findings provide valuable theoretical insights into the behavior of nonlinear wave phenomena in disciplines such as nonlinear optics, fluid dynamics, and quantum mechanics, particularly under temporally varying external influences.</p>