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.
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.
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.