Journal of Nonlinear Mathematical Physics

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Volume 28, Issue 1, March 2021, Pages 27 - 37

The (N + 1)-Dimensional Burgers Equation: A Bilinear Extension, Vortex, Fusion and Rational Solutions

Authors
Hongli An1, *, Engui Fan2, Manwai Yuen3
1College of Science, Nanjing Agricultural University, Nanjing 210095, People’s Republic of China
2School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
3Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, New Territories, Hong Kong
*Corresponding author. Email: kaixinguoan@163.com
Corresponding Author
Hongli An
Received 14 September 2019, Accepted 5 March 2020, Available Online 10 December 2020.
DOI
10.2991/jnmp.k.200922.004How to use a DOI?
Keywords
The (N + 1)-dimensional Burgers system; bilinear formulation; generalized Cole-Hopf transformation; vortex solutions; multiple fusion solutions; rational solutions
Abstract

In this paper, by introducing a fractional transformation, we obtain a bilinear formulation for the (N + 1)-dimensional Burgers equation. Such a formulation constitutes a bilinear extension to the (N + 1)-dimensional Cole-Hopf transformation between the (N + 1)-dimensional Burgers system and generalized heat equation. As applications of the bilinear extension to the Cole-Hopf transformation, four types of physically interesting exact solutions are constructed, which contain vortex solutions, multiple fusions, rational solutions and triangular rational solutions. The behaviors of these solutions are analyzed and simulated. Interestingly, the type of fusion solutions has recently found applications in organic membrane, macromolecule material, even-clump DNA, nuclear physics and plasmas physics et al.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 1
Pages
27 - 37
Publication Date
2020/12/10
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.k.200922.004How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Hongli An
AU  - Engui Fan
AU  - Manwai Yuen
PY  - 2020
DA  - 2020/12/10
TI  - The (N + 1)-Dimensional Burgers Equation: A Bilinear Extension, Vortex, Fusion and Rational Solutions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 27
EP  - 37
VL  - 28
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.200922.004
DO  - 10.2991/jnmp.k.200922.004
ID  - An2020
ER  -