Exploring stochastic dynamics with different wave structures for the Nizhnik–Novikov–Veselov system and their applications

The article is focused on the analysis of a mathematical model known as the Nizhnik–Novikov–Veselov (SNNV) system, which incorporates a specialized mathematical tool called the truncated M-fractional derivative (TMD). This model has broad applications in various scientific fields and considered an isotropic Lax extension of the one-dimensional Kdv equation which has diverse applications in the areas of warm ions, shallow water waves, electromagnetic signals, and river irrigation flows. To extract the solutions of the SNNV system, a modified version of the extended tanh-function method which is known as amended extended tanh-function method (AETF) is brought into play to derive solitary wave solutions for the SNNV system. These formulated solutions are categorized as trigonometric, exponential, and hyperbolic functions. For physical exemplification and knowledge of the dynamic physical features of the governing model, some reported solutions have been deliberated graphically by selecting appropriate parametric values. The computed outcomes have implications in diverse areas of applied sciences such as quantum mechanics, magneto-electrodynamics, heavy ion collisions, optical fiber technology and also opens doors to practical applications in diverse domains. The application of the AETF approach in this study demonstrates its efficiency and competence in scrutinizing and extracting soliton solutions in nonlinear partial differential equation.