Abstract
Solutions such as symmetric, bright soliton and periodic solutions play a prominent role in the field of differential equations, and they can be used to investigate several phenomena in nonlinear sciences. Some waves such as ion and magneto-sound waves in plasma are investigated by using some partial differential equations (PDEs) such as Novikov-Veselov (NV) equations. In this work, the improved
-expansion approach is utilized to extract numerous soliton solutions for NV system. Hamiltonian system is invoked to analyze the stability of some solutions. The finite difference approach is successfully applied to achieve the numerical simulations of the proposed equations. We also introduce the stability and the accuracy of the numerical scheme. In order to validate the correctness of the accomplished results, we compare the exact solutions with the numerical solutions analytically and graphically. The presented techniques are very convenient and adequate and can be employed to other types of nonlinear evolution equations.