1. Jun 8, 2008 #1

   mark gazi

   

   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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   mark gazi, Jun 8, 2008
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3. Jun 8, 2008 #2

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   The first thing you would do, of course, is separate into "u> 0", "u< 0" cases. After that it is pretty much standard.

    

   HallsofIvy, Jun 8, 2008
4. Jun 8, 2008 #3

   mark gazi

   

   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.

    

   mark gazi, Jun 8, 2008
5. Jun 9, 2008 #4

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   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.

    

   HallsofIvy, Jun 9, 2008

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