Parameter-driven stabilization of gradient-induced asymmetric solitons in PT-symmetric media: Comprehensive mapping of potential effects in 2D nonlinear waveguides

We investigate the propagation and stabilization of gradient-induced asymmetric solitons in a two-dimensional Modified Nonlinear Schrodinger (MNLS) framework with spatially varying nonlinearity. In the absence of external modulation, the asymmetry generates a transverse nonlinear momentum that drives the beam away from the center, producing both amplitude change and systematic drift. We show that a parity–time (PT) symmetric imaginary potential, introduced as a transverse gain—loss landscape, provides an effective mechanism to counteract this gradient-induced asymmetry. By modulating the parameter space of the steepening strength, imaginary-potential coefficient, real-potential depth, nonlinearity and diffraction parameter we identify unique points at which the nonlinear flux, diffraction, and PT −induced transverse energy exchange reach a well-defined balance condition. At these operating space, the soliton recovers a stable propagation state with suppressed drift, preserved beam width, and nearly constant amplitude. When the PT −symmetric potential strength is below or above this balancing value, the beam exhibits characteristic signatures such as spreading-dominated decay, oscillatory focusing–de focusing cycles, or residual amplification, depending on the relative dominance of system parameters. In addition, we demonstrate collision dynamics, a propagation-based perturbation study that directly reveals the dynamical stability of these beams, complementing and validating the parameter-controlled stability analysis. The results establish a comprehensive picture of how PT −symmetric gain–loss mechanisms can restore symmetry and stability in self-steepening optical solitons, and they provide guidelines for controlling nonlinear beam transport in engineered wave guiding structures with spatially modulated refractive index and nonlinearity.