A mathematician would say that any function of x and t in which these two
variables appear together as z=x-v*t is a one-dimensional wave propagating
to the right along the x axis. For example:
y=A*sin(x-v*t), y=A*(x-v*t)^2 or y=exp(x-v*t)
Each of them satisfies the differential wave equation. Neither energy nor
momentum appear in the definition. Note that y can be any quantity: the
displacement, pressure, E or B. Even the probability of finding a particle.
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A small quibble, this is a description of a traveling wave that retains its
shape (no dispersion). And shouldn't be taken as a complete exhausting of
the types of wave phenomena