Nonlinear Partial Differential Equation paid collaboration needed

Jobs
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I will pay $200 for the solution of the following nonlinear Partial Differential Equation using Wolfram Technologies:

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Hi @Tao, are you looking for numeric or exact symbolic solution? If numeric, would solutions for large enough (but not infinity) radius suffice as an approximation? If you have any other thoughts or background or references for this problem, it would be very helpful, as well as any initial setup in form of Wolfram Language code that you have may tried already.

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Open in Wolfram Cloud ↗
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I’m not a expert for solving this kind equation, but using FiniteElement method with coefficient = 3/2, I have:

     usol2 = Block[{\[Epsilon] = $MachineEpsilon, inf = 48, 
         coeff = 1 + 1/2}, 
        NDSolveValue[{I*
            D[M[r, t], 
             t] == (-E^-M[r, t])*(D[M[r, t], r, r] - (D[M[r, t], r])^2 + (
               2 D[M[r, t], r])/r) - 
            NeumannValue[M[r, t], r == \[Epsilon]], 
          DirichletCondition[M[r, t] == coeff*E^(-(r^2/2)), t == 0], 
          DirichletCondition[M[r, t] == 0, r == inf]}, 
         M, {r, \[Epsilon], inf}, {t, 0, 2}, 
         Method -> {"FiniteElement", "InterpolationOrder" -> {M -> 2}, 
           "MeshOptions" -> {"MaxCellMeasure" -> 2/100}}]];
     xv = NArgMax[Norm[usol2[0, t]], {t, 1/10, 5/10}];
     Show[Plot3D[2 Norm[usol2[r, t]], {r, 0, 3}, {t, 0, 2}, 
       PlotRange -> All, 
       AxesLabel -> {Style["r ", Italic], Style["t", Italic], 
         Rotate["\[LeftBracketingBar]M(r, t)\[RightBracketingBar]", \[Pi]/
          2]}, ViewPoint -> {3, -2.2, 4.1}, MaxRecursion -> 4], 
      ParametricPlot3D[{r, xv, 2 Norm[usol2[r, xv]]}, {r, 0, 3}, 
       PlotStyle -> Directive[Red, Thickness -> 0.005]]]

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Maybe you post question here ,you got a better answer.

Regards M.I.

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Hello Mariusz Iwaniuk,

Thank you for sharing your valuable information with me. I appreciate the time and effort you took to provide them.

Regards,
Tao Guo

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Hi @Sam, I apologize for the confusion! I realized that I responded to you in the wrong location.

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