i found solution of PDE but there is some different from my solution and paper solution so there is must be a mistake becuase he solved by maple too he mentioned in the paper i try to figure out but i can't see any mistake from my solution can anyone watch where i did mistake, i change some letter in finding parameter but they are same like p=k&h=A&n=p&w=n

here is paper solution 

parameter-different.mw

i want to plot density i try to use code of [interactive] but didn't give me density 

>  >  Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.   >  >  >  >  {x, y, a[0], k[2], p[1], p[2]}   >  P :=   [  a[0]=1.2, k[2]=0.8, p[1]=-0.8, p[2]=0.4] (1) >  latex(P) [a_{0} =  1.2, k_{2} =  0.8, p_{1} = - 0.8, p_{2} =  0.4]   >  Assume some functional form for U(xi) >    insert numerical values >  solnum :=subs(P, sol3); (2) >  cg0 = 0.3200000000e1 / ((0.4000000000e0 * x - 0.8e0 * y) ^ 2 + (0.8e0 * x + 0.4e0 * y) ^ 2 + 0.12e1) - 0.5120000000e1 * x ^ 2 / ((0.4000000000e0 * x - 0.8e0 * y) ^ 2 + (0.8e0 * x + 0.4e0 * y) ^ 2 + 0.12e1) ^ 2;   >    >  >  >  Warning, expecting only range variables [x, y] in expression density(3.200000000/((.4000000000*x-.8*y)^2+(.8*x+.4*y)^2+1.2))+density(-5.120000000*x^2/((.4000000000*x-.8*y)^2+(.8*x+.4*y)^2+1.2)^2) to be plotted but found name density   Warning, expecting only range variables [x, y] in expression contour(3.200000000/((.4000000000*x-.8*y)^2+(.8*x+.4*y)^2+1.2))+contour(-5.120000000*x^2/((.4000000000*x-.8*y)^2+(.8*x+.4*y)^2+1.2)^2) to be plotted but found name contour

Download graph-density-countour.mw

Download F-params.mw

there is must be a problem but i didn't figure out ?  in this command didn't give me my parameter why?
vars1 := indets(eqs1);
ans := solve(eqs1, {a[0], a[1], a[2], a[3], a[4], e[1], k[1], n[1], p[1]});

parameter.mw

Download polar.mw