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.
CitationAn, H., Fan, E., & Yuen, M. (2021). The (N + 1)-dimensional Burgers equation: A bilinear extension, vortex, fusion and rational solutions. Journal of Nonlinear Mathematical Physics, 28(1), 27-37. doi: 10.2991/jnmp.k.200922.004
- The (N + 1)-dimensional Burgers system
- Bilinear formulation
- Generalized Cole-Hopf transformation
- Vortex solutions
- Multiple fusion solutions
- Rational solutions