Show that each of these equations satisfies translational invariance

Show that each of these equations satisfies translational invariance, that is, if u(x,t) is a solution, then v(x,t)=u(x −φ,t) is also one.

Show that only the last equation satisfies Galilean invariance, that is, if u(x,t) is a solution, then v(x,t)=u(x −V t,t)−V is also one.


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