Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Abstract

A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation is considered, which can be used to describe many nonlinear phenomena in plasma physics. By virtue of binary Bell polynomials, a bilinear representation of the equation is succinctly presented. Based on its bilinear formalism, we construct soliton solutions and Riemann theta function periodic wave solutions. The relationships between the soliton solutions and the periodic wave solutions are strictly established and the asymptotic behaviors of the Riemann theta function periodic wave solutions are analyzed with a detailed proof.

Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

“…While figure 2 show the semi-analytical solution in three different forms (2D, 3D, and contour plots). Comparing our solution with the solutions obtained in previously published papers, it can be seen that our solution is completely different from the solution evaluated in [25][26][27][28][29].…”

“…Another goal of the manuscript is to limit the examination of the semi-analytical and numerical solutions of the considered model to an explanation of the accuracy of the analytical solutions obtained and the analytical schemes used [23,24]. The generalized CBS equation is given by [25][26][27][28][29][30]:…”

Fissionable wave solutions, lump solutions and interactional solutions for the (2 + 1)-dimensional Sawada–Kotera equation

“…We also obtain the elastic interaction of a lump and a solitary wave, and the elastic-fissionable-coexistence interaction of a lump and an (N -2)-fissionable wave. Based on the ideas of asymptotic analysis methods in [39][40][41][42], we give their asymptotic analyses of N-fissionable wave solutions, the elastic interaction of a lump and a solitary wave in theoretically and graphically. Finally, we give some conclusions in section 4.…”

Homoclinic breather waves, rogue waves and solitary waves for a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation

“…The first-order rational solution of the self-focusing nonlinear Schödinger equation was first found by Peregrine to describe the roguewaves phenomenon (Peregrine, 1983). Recently, by means of the Darboux transformation and Hirota bilinear method, rogue wave solutions have been investigated in many complex systems (Tao and He, 2012; Guo et al , 2012; Zhao and Liu, 2013; Yan et al , 2018b; Tian, 2018a; Wang et al , 2018b; Wang et al , 2018c; Qin et al , 2018a; Qin et al , 2018b; Wang et al , 2018a; Yan et al , 2018a; Dong et al , 2018; Feng et al , 2017b; Wang et al , 2017d; Feng and Zhang, 2018; Wang et al , 2017a; Wang et al , 2017b; Qin et al , 2018c; Chen et al , 2015a; Liu et al , 2015; Chen et al , 2015b).…”