Take the 2-minute tour ×  What does "no explicit time
dependence" mean in this context? :  A symmetry of the KdV is
given by $$\tilde x=x, \tilde t=t+\epsilon, \tilde u =u$$ as
there is no explicit time dependence in the KdV.  share|improve
this question add comment  1 Answer  up vote 1 down vote
accepted  In Physics, the notion of explicit time dependence
denotes equations where the time parameter t occurs "freely" and
not only as a $\frac{d}{dt}$. So an equation of the form
$v(x)=a_0t+v_0$ is explicitly time dependent, but $a(x)=a_0$ is
not.  share|improve this answer Thank you, Dominik. Just to
confirm my understanding of your explanation: the partial
derivative wrt $t$ does not count as explicitly time-dependent,
only an actual factor of $t$ in the equation does? –  Henry Nov
24 '12 at 19:59 That's right. Another commonly used word for
this is that the equation is autonomous, a word which for
unfathomable reasons doesn't appear in the wikipedia article on
differential equations. –  Harald Hanche-Olsen Nov