Analytical and Qualitative Investigation of the (2+1)$$ \left(2+1\right) $$‐Dimensional Stochastic Nizhnik–Novikov–Veselov System Under Multiplicative Noise

ABSTRACT In this study, we analyze the ‐dimensional stochastic Nizhnik–Novikov–Veselov (SNNV) system subjected to multiplicative noise in Itô sense. This expanded model holds significant relevance in simulating different physical phenomena, including shallow‐water waves, sound propagation, long internal waves in density‐stratified oceans, and ion‐acoustic waves in plasma through crystal lattices. To derive exact and diverse soliton solutions for the stochastic SNNV system, we use three powerful analytical techniques: the generalized Arnous method, the generalized multivariate exponential rational integral function method (gMERIFM), and the enhanced modified extended tanh function method (eMETFM). By employing these techniques, we construct a wide spectrum of stochastic wave structures, including bright solitons, dark solitons, combo solitons, M‐shaped waves, periodic waves, singular solutions, mixed trigonometric forms, and rational wave solutions. These findings demonstrate the model's capacity to accommodate rich and complex wave structures under the influence of stochasticity. In addition to the analytical treatment, we provide an in‐depth qualitative analysis to exhibit the dynamical properties of the system. This includes a comprehensive bifurcation analysis to reveal the critical transitions in system behavior. Moreover, the development and emergence of chaos are comprehensively studied using a suite of diagnostic tools: 2D phase portraits, time series analysis, Poincaré map, return map analysis, power spectral density, multistability analysis, Lyapunov exponent evaluation, fractal dimension estimation, strange attractor visualization, and multistability analysis. The integration of exact analytical solutions with qualitative and chaos analyses not only represents the versatility and robustness of the applied methods but also highlights the practical and theoretical significance of the stochastic SNNV system in modeling intricate physical environments. The findings contribute valuable insights into the nonlinear stochastic wave dynamics and lay a foundation for further studies in applied nonlinear science and mathematical physics.