Multiple rogue wave solutions of the (1+1)-dimensional Benjamin-Ono equation

Abstract

In this paper, by means of symbolic computation, we studied the multiple rogue wave (multi-RW) solutions of the (1+1)-dimensional Benjamin-Ono (BO) equation, which is used to describe one-dimensional deep water internal waves in mathematics. In order to achieve this goal, we used the bilinear neural network method to construct the superposition formulas of n-RW based on the bilinear form. Here we only showed 1-RW, 3-RW, and 6-RW solutions. The influence of the parameters in the solution expression upon the characteristics related to RW also was discussed. Then, the dynamics characteristics of the multi-RW solutions were analyzed by drawing the three-dimensional plot, contour plot, and density plot. We observed that m-RW consisted of m independent 1-RW. This interesting phenomenon helped us to better reveal the evolution mechanism of the (1+1)-dimensional BO equation.