Bright solitons of the variants of the Novikov-Veselov equation with constant and variable coefficients

In this paper, the existence of the bright soliton solution of four variants of the Novikov-Veselov equation with constant and time varying coefficients will be studied. We analyze the solitary wave solutions of the Novikov-Veselov equation in the cases of constant coefficients, time-dependent coefficients and damping term, generalized form, and in 1 + N dimensions with variable coefficients and forcing term. We use the solitary wave ansatz method to derive these solutions. The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Parametric conditions for the existence of the exact solutions are given. The solitary wave ansatz method presents a wider applicability for handling nonlinear wave equations.