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KdV equation

  1. Aug 8, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that the KdV has Galilean invariance.
    That is ut + 6uux + uxxx = 0 is invariant under the transformation xi = x - ct, tau = t, psi = phi - c/6


    2. Relevant equations



    3. The attempt at a solution
    Do we use the chain rule on these and plug into the KdV?
     
  2. jcsd
  3. Aug 9, 2011 #2

    HallsofIvy

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    Staff Emeritus
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    That would be what I would do. Essentially you just want to make that "change" of variables and show that you get exactly the same equation again. And changing variables in a differential equation involves the chain rule.
     
  4. Aug 9, 2011 #3
    Thanks.
    So d/dx = xix*d/dxi + taux*d/dtau = d/dxi
    and d/dt = xit*d/dxi + taut*d/dtau = -cd/dxi + d/dtau
     
  5. Aug 10, 2011 #4
    Got it.
    Thanks.
     
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