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The generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension has been investigated in this research. This model is used to elucidate how a magnetic field affects the weak ion-acoustic wave in the field of plasma physics. To deftly analyze the wide range of wave structures, we utilized the modified extended tanh and the extended rational sinh-cosh methods. Hyperbolic, periodic, and traveling wave solutions are presented as the results. Consequently, solitary wave solutions are also attained. This study shows that the solutions reported here are distinctive when our findings are contrasted against well-known outcomes. Moreover, realized findings are figured out in 3-dimensional, 2-dimensional, and contour profile graphs for the reader to comprehend their dynamics due to parameter selection. According to the findings, we can conclude that the suggested computational techniques are simple, dynamic, and well-organized. These methods are very functional for numerical calculations of complex nonlinear problems. Our results include a fundamental starting point in understanding physical behavior and the structure of the studied systems. [ABSTRACT FROM AUTHOR]

In this paper, some new exact traveling and oscillatory wave solutions to the Kudryashov-Sinelshchikov non-linear PDE are investigated by using Bernoulli sub-equation function method. Profiles of obtained solutions are plotted. [ABSTRACT FROM AUTHOR]