Study of the parametric effect of self-control waves of the Nizhnik-Novikov-Veselov equation by the analytical solutions

Abstract

A significant model of the preserved scalar nucleons associated with neutral scalar masons is the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation. Wave solutions are computed concerning exponential, hyperbolic and trigonometric structures balancing the powers in linear and nonlinear terms of the highest order from which scores of typical wave profiles including kink, bell-shape soliton, singular soliton, bright soliton, periodic soliton, dark soliton and dark-bright waves have been extracted. In this article, we have demonstrated that the nature of wave profiles fluctuates regarding the change of the free parameters associated with it and are principally controlled by the linear and nonlinear effect. The effects of other free parameters and wave velocity in the wave profile have also been discussed. The wave solutions are arranged through the improve Bernoulli sub-equation function (IBSEF) method and extending higher dimensional sine-Gordon expansion (SGE) method. Comparing the results obtained from both methods and analyzed the solutions by outlining figures for different values of corresponding variables, and it is detected that the attributes of those solutions are pivotal on the selection of parameters.