This study investigates various analytic soliton solutions of the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation in fluid dynamics and plasma physics using a recently introduced technique which is the New Kudryashov method. Moreover, it is examined how the wave propagation in both directions represented by the CBS equation occurs. The considered equation describes the interaction of the long propagating wave in the x axis with the Riemann propagating wave along the y axis. To get traveling wave solutions of the CBS equation, it is transformed into a nonlinear ordinary differential equation (NLODE) using a proper wave transformation. Supposing that the NLODE has some solutions in the form provided by the method, one can obtain a nonlinear system of algebraic equations. The unknowns in the system can be found by solving the system via computer algebraic systems such as Mathematica and Maple, etc. Substituting the unknowns into the trial solutions provided by the method, we get the solutions of the NLODE. Then, putting wave transformations back into the solutions of NLODE, we get the solutions of the considered CBS equation. We present the 2D, 3D and contour plots to illustrate the physical behavior of the obtained solutions using the appropriate parameters. Besides, the schematic representation of wave motion of the soliton along both spatial axes and its interpretation are given. The used novel technique can be used for a wide range of partial differential equations (PDEs) in the real world. It is expected that the derived soliton solutions might be helpful for better understanding the wave behavior and so, it might contribute to future studies in various disciplines.