Abstract
In this article, we have achieved new solutions for the Novikov-Veselov system using several methods. The present solutions contain soliton solutions in the shape of hyperbolic, rational, and trigonometric function solutions. Magneto-sound and ion waves in plasma are examined by employing partial differential equations, such as, the Novikov-Veselov system. The Generalized Algebraic and the Modified F-expansion methods are employed to achieve various soliton solutions for the system. The finite difference method is well applied to convert the proposed system into numerical schemes. They are used to obtain the numerical simulations for NV. I also present a study of the stability and Error analysis of the numerical schemes. To verify the validity and accuracy of the exact solutions obtained using exact methods, we compare them with the numerical solutions analytically and graphically. The presented methods in this paper are suitable and acceptable and can be utilized for solving other types of non-linear evolution systems.