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Characteristics/solving of PDE's

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Question attached

    2. Relevant equations

    3. The attempt at a solution

    So I attempt to just do a), b), c) in one systematic way, however, I'm following examples which I don't quite understand. I have also attached the start of the problem which I'm trying to follow.

    I started off finding the characteristics which in this case, are

    dt/dtau = 1 , dx/dtau = -u^2 , du/dtau = 0

    solving these, I get t=tau, x=-G(Xi)^2*tau+Xi , u=G(Xi)

    now here is where I get stuck and confused by the example I'm following, I know how they got the first and last entry, but am confused how they got (1+/- Xi)tau+Xi.

    If someone can give me a hint/tip on where to go from here, or how to obtain each of the solutions of (-1/2, 1 and 1/2) via the coordinates Xi and tau, would be much appreciated.

    Attached Files:

  2. jcsd
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