Rational solutions and interaction solutions for a fourth-order nonlinear generalized Boussinesq water wave equation

Abstract 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. Compare with the published literatures, some completely new results are presented in this paper.