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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.

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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.

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    Thank you, @$H$arald$H$anche-Olsen !2012-11-24