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How to solve this non-linear PDE?

  1. Sep 15, 2009 #1
    I am new to non-linear PDEs. So I tried to solve it, but I stuck in the beginning.

    [tex]U^2_xU_t - 1 = 0[/tex]

    [tex]U(x, 0) = x[/tex]
     
  2. jcsd
  3. Oct 5, 2009 #2
    The equation admits a separation of variables, and the solution can be written as U(x,t)=f(x)+g(t). Inserting this, you get f'(x)^2=1/g'(t)=constant. The solution can then be checked to be U=x+t
     
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