Discrete analogue of the Burgers equation

作者：Ben Naim E^*; Krapivsky P L

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(45): 455003.

DOI：10.1088/1751-8113/45/45/455003

We propose the set of coupled ordinary differential equations dn(j)/dt = n(j-1)(2) - n(j)(2) as a discrete analogue of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the discrete system capture major features of their continuous counterpart. In particular, the propagation velocity of a traveling wave and the shape of a triangular wave match the continuous behavior. However, there are some subtle differences. For traveling waves, the propagating front can be extremely sharp as it exhibits double exponential decay. For triangular waves, there is an unexpected logarithmic shift in the location of the front. We establish these results using asymptotic analysis, heuristic arguments, and direct numerical integration.

• 出版日期2012-11-16