A nonlinear partial differential equation combining with a third-order derivative of the time variable $D_x{D}_t^3$ is studied. By adding a new fourth-order derivative term, its lump solutions are explicitly constructed by the Hirota bilinear method and symbolic computation. Furthermore, the effect of the new fourth-order derivative term on the solution is discussed. The dynamical behaviors of two particular lump solutions are analyzed with different choices of the parameters.

中文翻译：

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包含时间三阶导数的非线性PDE的总解

非线性偏微分方程和时间变量的三阶导数 $d_X{d}_{Ť}^3$被研究。通过添加一个新的四阶导数项，它的总解由Hirota双线性方法和符号计算显式构造。此外，还讨论了新的四阶导数项对解的影响。使用不同的参数选择来分析两个特定的整体解决方案的动力学行为。