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How to solve the following equation ?

  1. Jun 8, 2008 #1
    It is a nonliear Partial differential equation . you can find it in the appendix.
    If you have some good idea about this equation ,ok ,please reply to me .thanks!
     

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  3. Jun 8, 2008 #2

    HallsofIvy

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    The first thing you would do, of course, is separate into "u> 0", "u< 0" cases. After that it is pretty much standard.
     
  4. Jun 8, 2008 #3
    My question

    First, thank you .but if the solution of the equation (U) is a complex number, how to separate the "u" into the two condition:(1) U>0; (2) U<0.
     
  5. Jun 9, 2008 #4

    HallsofIvy

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    If u is a complex valued function, then separate it into real and imaginary parts: u(x)= p(x)+ i q(x). |u|2= p2+ q2 and you have two non-linear differential equations for p and q. They will still be rather nasty I am afraid. MOST non-linear equations can be solved in closed form.
     
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