Steps_1_and_2_DAH2.mw

@salim-barzani I updated Step1_DAH.mw - please check the statement in bold is correct. I will look at step 2.

@salim-barzani The errors in pdes-s-1-2.mw and step1-2.mw are because coeff can only handle integer powers, not symbolic ones. The findexp routine can handle symbolic powers.

@salim-barzani Thanks for the detailed explanation. I have finished inplementing step 1 for this case, but I still don't know how "higher nonlinearity" is defined in the general case. I will ok at the next steps later.

Step1_DAH.mw

@salim-barzani I did some more, but I still don't know how to complete step 1.

new-p_DAH.mw

@salim-barzani You say "is clear what they did". Would you please explain the steps to find alpha[1]. I do not understand that (and extra papers just seem to say the same thing). 

I don't understand what is happening, but maybe this is helpful as a start.

p1_DAH.mw

@michele @Carl Love's commands only work for 1-D input. I'm guessing you are using 2-D input, so the equivalent commands are

M[.., -[$1..n]]

M[-[$1..n]]

It can be quite difficult to get such complicated expressions into exactly the form you want in a paper. My usual procedure is the take the Maple expression A, copy it and modify it by hand to the way you want it, set it to B, and then simplify(A-B) to check that you haven't made a mistake.

@michele 
In U[.., p], the ".." means select all the rows (short for 1..4 in this case), and p is a list of columns to select, so for p=[4,3,2,1] the 4th, then 3rd then 2nd then first columns are selected.

See the help page ?MVselect for more details.

@michele (doesn't dispay correctly here)

Download EvecsSorted.mw

@michele I'm not clear how you generated your matrix, since you didn't upload your worksheet. If M is your Matrix, you can convert it to symmetric by

M := Matrix(M, shape = symmetric);

@salim-barzani Here's an attempt that circumvents the problem, but I would guess that your H is not actually a solution of the pde.

n1.mw

Edit - I really don't understand what is happening to the integrals there; in particular how the integration constants are dealt with in a consistent way.

@Alex0099 As far as I know, Maple does not have specific support for Green's functions. One just solves the equations with Dirac, as you did. You may or may not get a solution, depending on how difficult the problem is. Here are some examples in cartesian coordinates, which illustrate varying degrees of success.

Download Dirac.mw

Do you have a functional form of source term in mind for which the Green's function is just an intermediate step, or is the Green's function itself the objective? If you can bypass it that might be easiest.

@Alex0099 The error is because you used floating point 1.1 and 0.5 instead of 11/100 and 1/2. But since you want a symbolic solution, I would leave these as eta1 and eta2.

I'm not clear how much you want to help Maple along. In general pdsolve is not good with ICs/BCs and I would seek a general solution first and then apply the ICs/BCs afterward. It looks like it doesn't find a general solution with the source term. You could try more specific hints, but in the absence of that I would probably follow along with the procedure you gave in the earlier worksheet, but for the specify sinh(xi) etc BCs.

bc4 still needs some work. You want the integrated flux oround the two perimeters equal? In any case you should use D and not diff for the bcs.

PDE_upd_2.mw