Rogue Wave and Multiple Lump Solutions of the (2+1)‐Dimensional Benjamin‐Ono Equation in Fluid Mechanics

Abstract

In this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. The 3-lump solutions, 6-lump solutions, and 8lump solutions are presented, respectively. The 3-lump wave has a "triangular" structure. The centers of the 6-lump wave form a pentagram around a single lump wave. The 8-lump wave consists of a set of seven first order rogue waves and one second order rogue wave as the center. The multiple lump wave develops into low order rogue wave as parameters decline to zero. The method presented in this paper provides a uniform method for investigating high order rational solutions. All the results are useful in explaining high dimensional dynamical phenomena of the (2+1)-dimensional Benjamin-Ono equation.

Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

“…[19], a symbolic computation approach was proposed by Zha. Multiple rogue wave solutions of many NPDEs have been discussed by using the symbolic computation approach [27][28][29][30][31]. Here, we want to make a slight adjustment to this method as follows…”

“…Based on previous literature and modified symbolic computation approach [27][28][29][30][31], assume…”

Breather Wave and Traveling Wave Solutions for A (2 + 1)-Dimensional KdV4 Equation

“…In the research of nonlinear science, more and more attention has been paid to the nonlinear evolution equations [1][2][3], which can depict many important phenomena in physics and other related fields. In order to describe these nonlinear phenomena, it is very necessary to seek exact solutions for nonlinear evolution equations in mathematical physics [4][5][6].…”

New Complex Solutions to the Nonlinear Electrical Transmission Line Model

“…Atte Aalto and Jarmo Malinen have introduced that wave propagation on networks solvable (forward in time) and energy passive or conservative with the help of a theoretical approach [6]. Therefore, many novel models have been presented to the literature by many scientists [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”