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I'm really interesting to know more about Plasma physics for waves , it comes in my mind to ask this question related to dispertion relation topic exactly plane waves , It is well known that the plane waves defined by the following mathematical formula : $A(x,t)= A_0 \exp (2i\pi (\frac{x-vt}{\lambda}))$

$A$ is the amplitude of the wave, $A_0 = A(0,0)$

$x$ is a position along the wave's direction of travel, and $t$ is the time at which the wave is described. Now my question here is : if we take other plane wave:$A'(x,t)= A_0 \exp (2i\pi (\frac{x-vt}{\lambda}))$ $A'(x,t)= A'_0 \exp (2i\pi (\frac{x-vt}{\lambda}))$ and we look to do mathematical composition of $ A'$ and $ A $ like this : $(A'\circ A)(x,t) $, Now does this composition give us a plane wave ? and if it is What about its new parameters ?

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    $\begingroup$ Composition is meaningless here. Composition means taking the output of one function and using it as the input for another function. That doesn’t work here because the output is not $x$ and $t$. Perhaps you are confusing composition with superposition, which means simply adding the two waves together? $\endgroup$ – G. Smith Dec 18 '19 at 21:53
  • $\begingroup$ @G.Smith, I do not mean superposition, But I meant what composition operation give us between two plane waves and pleas could u explaine me more why the output is not x and y ? $\endgroup$ – zeraoulia rafik Dec 18 '19 at 22:05
  • $\begingroup$ The output is the intensity of the wave at a point in space and time. That intensity is neither $x$ nor $t$ and cannot be fed into the other wave formula. $\endgroup$ – G. Smith Dec 18 '19 at 22:07
  • $\begingroup$ If you think composition has meaning here, try writing down $(A'\circ A)(x,t) $ as an explicit function of $x$ and $t$. $\endgroup$ – G. Smith Dec 18 '19 at 22:13
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    $\begingroup$ With all due respect, your understanding is wrong. Talking about the composition of these two functions is literally nonsense. See en.wikipedia.org/wiki/Function_composition. $\endgroup$ – G. Smith Dec 18 '19 at 22:24

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