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<p>In this study, we aim to present a deeper exploration of the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) for fluid dynamics. The travelling wave transformation, along with the semi-inverse method (SIM) are utilised to develop the variational principle (VP). In light of the VP, the Hamiltonian is found. Upon the planar dynamical system that is constructed through the Galilean transformation, the phase portraits are illustrated, and the conditions for the existence of solutions with different waveform structures are expounded by conducting the bifurcation analysis. Meanwhile, the system’s chaotic behaviours are also analysed. In the end, two robust schemes are employed to investigate various wave solutions: the variational approach (VA), which combines the VP and Ritz technique and the Hamiltonian-based approach (HBA), based on the energy conservation law. These different solutions include the kink solitary, anti-kink solitary and periodic wave solutions. Correspondingly, the waveforms of the obtained solutions are depicted graphically to exhibit the physical properties. To the author's knowledge, the quantitative analysis has not been reported yet and the VA and the HBA have not been used to explore the considered equation so far.</p>

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Chaotic pattern, phase portrait, bifurcation analysis, variational principle, Hamiltonian and diverse wave solutions of the generalised (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Yan-Hong Liang,
  • Kang-Jia Wang

摘要

In this study, we aim to present a deeper exploration of the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) for fluid dynamics. The travelling wave transformation, along with the semi-inverse method (SIM) are utilised to develop the variational principle (VP). In light of the VP, the Hamiltonian is found. Upon the planar dynamical system that is constructed through the Galilean transformation, the phase portraits are illustrated, and the conditions for the existence of solutions with different waveform structures are expounded by conducting the bifurcation analysis. Meanwhile, the system’s chaotic behaviours are also analysed. In the end, two robust schemes are employed to investigate various wave solutions: the variational approach (VA), which combines the VP and Ritz technique and the Hamiltonian-based approach (HBA), based on the energy conservation law. These different solutions include the kink solitary, anti-kink solitary and periodic wave solutions. Correspondingly, the waveforms of the obtained solutions are depicted graphically to exhibit the physical properties. To the author's knowledge, the quantitative analysis has not been reported yet and the VA and the HBA have not been used to explore the considered equation so far.