A bilinear form of the (2þ1)-dimensional nonlinear Calogero-Bogoyavlenskii-Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter. This parameter can control the direction, wave height and angle of the traveling wave. Based on the Hirota bilinear form and ansatz functions, we build many types of novel structures and manifold periodic-soliton solutions to the CBS model. In particular, we obtain entirely exciting periodic-soliton, cross-kinky-lump wave, double kinky-lump wave, periodic cross-kinkylump wave, periodic two-solitary wave solutions as well as breather style of two-solitary wave solutions. We present their propagation features via changing the existence parametric values in graphically. In addition, we estimate a condition that the waves are propagated obliquely for η 6 ¼ 0 , and orthogonally for η ¼ 0.
Under examination in this manuscript is a (2+1)-D generalized Calogero–Bogoyavlenskii–Schiff equation is considered through a criterion variable transition in which a dominating variable involved. Based on the Hirota bilinear method, we build novel structures entirely innovative lump solutions, periodic solutions in separable form, and periodic-soliton solutions and also perforated appearance of two-solitary wave are obtained. Furthermore, we demonstrate that the constraints that lump solutions meet are through to satisfy a number of significant features, such as navigation, polarity and nonlinear analysis. With the aid of Maple, the 3-D plot and contour plot, the physical properties of these vibrations are very effectively explained. The obtained results can improve the dynamics of higher-dimensional nonlinear water wave’s scenarios in fluids and plasma phenomena.
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