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This study aims to investigate the (3+1)-dimensional fourth-order KdV-type hierarchy nonlinear equation. For this aim, we use Hirota’s simple method to handle one, two, three, and four soliton solutions. Furthermore, using the ansatz method in the form of the tanhp function, the symbolic computational method is used to construct kink solitary wave solutions, multi-wave solutions, X-type solitons, and Y-type solitons, as well as shock wave solutions. Furthermore, the physical structure and propagation characteristics of the obtained solutions are simulated. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. |
