Exploration of solitary waves and periodic optical soliton solutions to the nonlinear two dimensional Zakharov–Kuzetsov equation

In this research work, we explored the unexpected optical soliton and solitary wave to the nonlinear (2+1)-dimensional Zakharov–Kuzetsov equation by utilizing the auxiliary equation method. The explored optical soliton and solitary wave solutions obtained in variety of soliton including bright solitons, anti-kink wave solitons, periodic optical solitons, kink wave solitons, dark solitons, anti-kink dark solitons, combined solitons, crest-turf form solitons, peakon solitons and periodic solitary waves. The physical structure of extracted optical solitons visualized in three-dim, two-dim and contour plotting by utilizing the numerical simulations with computational software Mathematica. The secured optical solitons will be play important role in the investigation of nonlinear (2+1)-dim Zakharov–Kuzetsov equation and will be develop interest in the researchers for further investigation on this nonlinear model. The physical structure of explored soliton results show that, these solitons will be play important role in the areas of sciences and engineering such as nonlinear optics, transmission system, communication system, nonlinear dynamics, soliton wave theory and ocean engineering. The successful investigation is the witness that the proposed approach is effective, efficient and powerful for the exploration of solitary waves special verities of optical solitons to the various kinds of nonlinear evolution equations.