TY - JOUR
T1 - Generation of nonlinear evolution equations by reductions of the Self-Dual Yang - Mills equations
AU - Zhang, Yu Feng
AU - Tam, Hon Wah
N1 - Supported by the Fundamental Research Funds for the Central Universities (2013XK03) and the National Natural Science Foundation of China under Grant No. 11371361.
PY - 2014/2
Y1 - 2014/2
N2 - 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.
AB - 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.
KW - integrable coupling
KW - Lax pair
KW - self-dual Yang-Mills equation
UR - http://www.scopus.com/inward/record.url?scp=84897502062&partnerID=8YFLogxK
U2 - 10.1088/0253-6102/61/2/10
DO - 10.1088/0253-6102/61/2/10
M3 - Journal article
AN - SCOPUS:84897502062
SN - 0253-6102
VL - 61
SP - 203
EP - 206
JO - Communications in Theoretical Physics
JF - Communications in Theoretical Physics
IS - 2
ER -