Lie symmetries, Q-conditional symmetries, and exact solutions of nonlinear systems of diffusion-convection equations

被引：0
作者：
M. I. Serov
R. M. Cherniha
机构：
[1] Poltava Technical University, Poltava
[2] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev
来源：
Ukrainian Mathematical Journal | 2003年 / 55卷 / 10期
关键词：
Exact Solution; Nonlinear System; Evolution Equation; Arbitrary Function; Symmetry Property;
D O I：
10.1023/B:UKMA.0000022071.88943.51
中图分类号：
学科分类号：
摘要：
A complete description of Lie symmetries is obtained for a class of nonlinear diffusion-convection systems containing two Burgers-type equations with two arbitrary functions. A nonlinear diffusion-convection system with unique symmetry properties that is simultaneously invariant with respect to the generalized Galilei algebra and the operators of Q-conditional symmetries with cubic nonlinearities relative to dependent variables is found. For systems of evolution equations, operators of this sort are found for the first time. For the nonlinear system obtained, a system of Lie and non-Lie ansätze is constructed. Exact solutions, which can be used in solving relevant boundary-value problems, are also found. © 2003 Plenum Publishing Corporation.
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页码：1619 / 1638
页数：19
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