科研之友
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摘要
We introduce an inhomogeneous term, f (t, x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f (t, x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra sl (2, R). When f is a function of only t, there are five symmetries with the algebra sl (2, R) circle plus(s) 2A(1). In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.
- 出版日期2017-5
