Department of Computer Science
Generation of nonlinear evolution equations by reductions of the self-dual Yang-Mills equations
With the help of some reductions of the self-dual Yang Mills (briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of (2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new (2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of (2 + 1)-dimensional integrable couplings of a new (2 + 1)-dimensional integrable nonlinear equation. © 2013 Chinese Physical Society and IOP Publishing Ltd.
integrable coupling, Lax pair, self-dual Yang-Mills equation
Source Publication Title
Communications in Theoretical Physics
Zhang, Yu-Feng, and Hon-Wah Tam. "Generation of nonlinear evolution equations by reductions of the self-dual Yang-Mills equations." Communications in Theoretical Physics 61.2 (2014): 203-206.