The (N + 1)-Dimensional Burgers Equation: A Bilinear Extension, Vortex, Fusion and Rational Solutions
- 10.2991/jnmp.k.200922.004How to use a DOI?
- The (N + 1)-dimensional Burgers system; bilinear formulation; generalized Cole-Hopf transformation; vortex solutions; multiple fusion solutions; rational solutions
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.
- © 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
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 -