Consider the Schrodinger equation $i\partial_t u=-\Delta u.$ Special solutions of the form $$u(t,x)=u_k(x)e^{ikt}$$ have many names which I've seen used, such as stationary states, solitons, standing waves, etc. I am wondering what one would call such a solution to the wave equation $\partial_t^2u=\Delta u.$ If it matters, assume that the spatial domain is unbounded. I suppose one could call them a mode solution since they feature a particular Fourier mode...

Consider the Schrodinger equation $i\partial_t u=-\Delta u.$ Special solutions of the form $$u(t,x)=u_k(x)e^{ikt}$$ have many names which I've seen used, such as stationary states, solitons, standing waves, etc. I am wondering what one would call such a solution to the wave equation $\partial_t^2u=\Delta u.$ If it matters, assume that the spatial domain is unbounded. I suppose one could call them a mode solution since they feature a particular Fourier mode.