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Solutions of the wave equation's little brother

  1. Sep 21, 2006 #1

    quasar987

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    Suppose I showed that a function f(z,t) of which I do not know the form explicitely satisfies the following pde:

    [tex]\frac{\partial f}{\partial z}=-\frac{1}{v}\frac{\partial f}{\partial t}[/tex]

    While it is certain that functions of the type g(z-vt) are solutions to the pde, does it mean that my f(z,t) is of this form necessarily?
     
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  3. Sep 21, 2006 #2

    Astronuc

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    Well, one could try a general solution

    [tex]f(z,-vt)\,=\,g(z)h(-vt)[/tex] and see where that takes one.
     
  4. Sep 21, 2006 #3

    quasar987

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    One understand that general solutions to pde are quite different from general solution to ode and one has no experience in dealing with the former.
     
  5. Sep 22, 2006 #4

    HallsofIvy

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    Since that is a linear equation, solutions may also be any sum of functions of that type.
     
  6. Sep 22, 2006 #5

    LeonhardEuler

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    But sums of functions of that type are also functions of that type.
     
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