High-order lumps, high-order breathers and hybrid solutions for an extended (3 + 1)-dimensional Jimbo–Miwa equation in fluid dynamics

Under investigation in this letter is an extended (3 + 1)-dimensional Jimbo–Miwa (eJM) equation, which can be used to describe many nonlinear phenomena in mathematical physics. With the aid of Hirota bilinear method and long-wave limit method, M -order lumps which describe multiple collisions of lum...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2020-03, Vol.100 (1), p.601-614
Main Authors: Guo, Han-Dong, Xia, Tie-Cheng, Hu, Bei-Bei
Format: Article
Language:English
Subjects:
Automotive Engineering
Breathers
Classical Mechanics
Computational fluid dynamics
Control
Dynamical Systems
Engineering
Mathematical analysis
Mechanical Engineering
Nonlinear phenomena
Original Paper
Propagation velocity
Solitary waves
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Under investigation in this letter is an extended (3 + 1)-dimensional Jimbo–Miwa (eJM) equation, which can be used to describe many nonlinear phenomena in mathematical physics. With the aid of Hirota bilinear method and long-wave limit method, M -order lumps which describe multiple collisions of lumps are derived. The propagation orbit, velocity and extremum of the 1-order lump solutions on ( x ,  y ) plane are investigated in detail. Resorting to the extended homoclinic test technique, we obtain the breather–kink solutions, rational breather solutions and rogue wave solutions for the eJM equation. Meanwhile, through analysis and calculation, the amplitude and period of breather–kink solutions increase with p increasing and the extremum of rational breather solution and rogue waves are also derived. T -order breathers are obtained by means of choosing appropriate complex conjugate parameters on N -soliton solutions. Periods of the 1-order breather solutions on the ( x ,  y ) plane are determined by k 12 and k 12 p 11 + k 11 p 12 , while locations are determined by k 11 and k 11 p 11 - k 12 p 12 . Furthermore, hybrid solutions composed of the kink solitons, breathers and lumps for the eJM equation are worked out. Some figures are given to display the dynamical characteristics of these solutions.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05514-9