Bright, periodic, compacton and bell-shape soliton solutions of the extended QZK and (3 + 1)-dimensional ZK equations

The (3 + 1)-dimensional Zakharov–Kuznetsov (ZK) and the new extended quantum ZK equations are functional to decipher the dense quantum plasma, ion-acoustic waves, electron thermal energy, ion plasma, quantum acoustic waves, and quantum Langmuir waves. The enhanced modified simple equation (EMSE) method is a substantial approach to determine competent solutions and in this article, we have constructed standard, illustrative, rich structured and further comprehensive soliton solutions via this method. The solutions are ascertained as the integration of exponential, hyperbolic, trigonometric and rational functions and formulate the bright solitons, periodic, compacton, bell-shape, parabolic shape, singular periodic, plane shape and some new type of solitons. It is worth noting that the wave profile varies as the physical and subsidiary parameters change. The standard and advanced soliton solutions may be useful to assist in describing the physical phenomena previously mentioned. To open out the inward structure of the tangible incidents, we have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the EMSE technique for extracting soliton solutions to nonlinear evolution equations is efficient, compatible and reliable in nonlinear science and engineering. (paper)