In this study, the third-order nonlinear (2+1)-dimensional Novikov-Veselov system of equations with constant coefficients has been investigated using an appropriate traveling wave transformation. The extended rational sin−cos technique and the modified exponential function method are two reliable and powerful methods that have been used for the specified nonlinear system. The main goal is to get valuable, exact traveling waves, periodic waves, and soliton solutions. The resulting solutions are expressed as a variety of trigonometric functions, including hyperbolic trigonometric functions, exponential functions, and rational functions. In that they provide light on the pertinent facets of the physical phenomenon, the suggested solutions are both innovative and significant. The properties of the solutions have been illustrated in a variety of figures, including two- and three-dimensional ones, to ensure the best visual assessment. Furthermore, two-dimensional graphs demonstrated how temporal development affects solution structures. The most powerful and efficient technologies are the computer software tools we use to create solutions and graphs.
Muhamad et al. (2026) studied this question.