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

被引：0
作者：
Hongli An
Engui Fan
Manwai Yuen
机构：
[1] Nanjing Agricultural University,College of Science
[2] Fudan University,School of Mathematical Sciences
[3] The Education University of Hong Kong,Department of Mathematics and Information Technology
来源：
Journal of Nonlinear Mathematical Physics | 2021年 / 28卷
关键词：
The (; + 1)-dimensional Burgers system; bilinear formulation; generalized Cole-Hopf transformation; vortex solutions; multiple fusion solutions; rational solutions; 35D99; 35C05; 35C99;
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学科分类号：
摘要：
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.
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页码：27 / 37
页数：10
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