Localized waves and interaction solutions to an integrable variable coefficients Jimbo-Miwa equation

Abstract

In this paper, the reduced variable coefficients Jimbo-Miwa (vcJM) equation is studied. Firstly, the integrability of the reduced vcJM equation is verified by Painleve analysis. Based on the Hirota bilinear method and the long wave limit method, the N-soliton solutions, rational and semirational solutions of the vcJM equation are obtained. By choosing different parameters and coefficient functions, four different kinds of local waves, including of solition, breather wave, lump and rogue waves, of the equation are obtained. Furthermore, the interaction solutions between different local waves are obtained. The dynamical behavior of the interaction between different local waves is studied by modifying the time parameters and the process is displayed by figures.

Various nonlinear characteristics of breather/rogue waves and controllable interaction phenomena for a new KdV equation with variable coeffcients

“…In the past decades, many excellent methods have been developed to construct exact solutions, such as the inverse scattering transform [20], Darboux transformation [21,22], Hirota bilinear theory [23,24], Lie group method [25], and so on. In recent years, Zhang [26][27][28] proposed a bilinear neural network method (BNNM) to find the exact solutions of NLPDEs.…”