<p>This study presents a comprehensive investigation into the propagation dynamics of solitonic beams in the form of a doughnut beam with a 10-micron beam width through negative nonlinear Kerr media. Our findings reveal novel insights into the effects of initial curvature of the beam front and loss/gain on beam propagation, demonstrating that solitonic behavior is significantly influenced by these parameters. Notably, we show that introducing gain to the medium can counterbalance the defocusing tendency of the beam, enabling nearly solitonic propagation over longer distances. In contrast, loss in the medium leads to defocusing, while initial curvature of the beam front induces complex focusing and defocusing dynamics. Employing a novel parabolic equation approach, we efficiently capture the underlying physics, bypassing unnecessary complexities. Our findings have important implications for the design and optimization of nonlinear optical systems, highlighting the potential for precise control of nonlinearity to stabilize beam propagation and mitigate beam divergence. This work provides new understanding of solitonic beam propagation, paving the way for soliton-based applications.</p>