The bilinear form of a fourth-order nonlinear generalized Boussinesq water wave equation is presented by using the Hirota’s bilinear method. Based on the presented bilinear form, some rational solutions and interaction solutions are obtained by choosing four class of test functions. The features such as the extreme values and asymptotics of the solutions are investigated and the three-dimensional plots and contour plots are drawn by selecting the appropriate parametric values. Compared with the published literatures, some completely new results are presented in this paper.

中文翻译：

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四阶非线性广义Boussinesq水波方程的有理解和相互作用解

利用Hirota's双线性方法，给出了四阶非线性广义Boussinesq水波方程的双线性形式。在给出的双线性形式的基础上，通过选择四类测试函数可以获得一些有理解和相互作用解。研究了溶液的极值和渐近性等特征，并通过选择适当的参数值来绘制三维图和轮廓图。与已发表的文献相比，本文提出了一些全新的结果。