Bifurcation is one of the most common phenomena in nature. We report a class of novel bifurcation phenomena in fluids by studying the bifurcation soliton solutions of an extended Kadomtsev–Petviashvili equation. By introducing the bilinear method and choosing appropriately the auxiliary function involved in the bilinear form, new soliton solutions are obtained. A further analysis shows there are interesting single- and multiple-bifurcation phenomena for the solutions, which can be used to depict the inelastic collision, fission and fusion dynamical behavior in fluids. Moreover, we illustrate that the bifurcation behavior is nonlinear because the amplitude of the soliton before the bifurcation is not equal the sum of the amplitudes of the two solitons after the bifurcation. This research can effectively simulate the bifurcation and merging phenomena in the fluid.

分岔是自然界中最常见的现象之一。我们通过研究扩展 Kadomtsev-Petviashvili 方程的分岔孤子解，报告了流体中一类新的分岔现象。通过引入双线性方法并适当地选择双线性形式涉及的辅助功能，获得了新的孤子溶液。进一步的分析表明，解存在有趣的单分岔和多分岔现象，可用于描述流体中的非弹性碰撞、裂变和聚变动力学行为。此外，我们说明分叉行为是非线性的，因为分叉前孤子的振幅不等于分叉后两个孤子的振幅之和。