@acer  i delete becuase in top write dublicate question and becuase of that no one answer for sure i will not lose you, i love you ... i hope to get best code

@acer  is been a week i am stuck at this step and i did for a lot of simple example without have the complex term, this is a link of question

https://www.mapleprimes.com/questions/240473-How-Substitute-Function-In-Iteration-

and again i will uploaded for you here maybe you can hundle this  you are powerfull 

i want something like this 

Ex.3.2.mw

@acer i  if you watch the first u[1] is wrong and also the answer is so different from the paper result i don't know even why he change the exponential term to function of sin and cos this is answer of paper 

@janhardo  watch k6 there is just one step remain 

@mmcdara  just one step remain which removing this conjugate  and iteration not work? 

k6.mw

@mmcdara this question i asked about a week ago but no one answer me except Dr.David but he have some work in last comment he mention that, i want to solve this  by taking Laplace adomian decomposition method but some issue appear for me i know each step do it by hand step by step and do it maple even but is need so much time for calculating all term one by one becuase of that i want to do systematically and  automatically  do all calculation i did a great program for that but as i mention in my adomian polynomial which is A[i] some term like abs(U)^2 appear which not remove by my loop and after that when i want to find iteration of approximate solution  again there is another problem appear which is conjugate(u) appear i want to remove that in my iteration too, i will put my figure of solution in here for more undrestand and there is a problem in naming letter of your code in A[i] this (i) not change i will mention in last picture
also i have more easy example which i solved automatically i will put the file if needed please mention ?

Re-Issue-mmcdara.mw

@mmcdara i belive that your coding is special and is very powerfull which can hundle %90 percent of programing, and still  there are a lot code of yours which i used , i hope participate my question and give us a chance to see your technique , thank you .

@janhardo  is wrong is not like that , is so different 

@mmcdara you are right about my answer but  i am not sure i am wrong or answer of him is wrong , thank you for your answer is been a while you didn't answer my question  i think you are mad at me?

@janhardo  we have some stuff  like conjugate(U[i](x,t)) and diff(U[i](x,t),x) and diff(conjugate(U[i](x,t)),x) i have to seperate this |U[i](x,t)|^n=U[i](x,t)*comjugate(U[i](x,t)) i know this but in coding i don't know how do that becuase if i don't seperate this i can't get my solution i did a lot of example but thus example don't have thus term if i can do this step the whole procecure will be end

@janhardo  i try use Ai but didn't give me anything usefull , when i test all of them give me error

@dharr i try to explain more in here step by step , i hope this time undrestand otherwise i have to send you a easy paper with solution , if you try use my first code which just u remain to put inside u[i] and do magic stuff like assume real or something like that maybe work , take your time i will be wait 

fully_explain.mw

@dharr is not just about u_xx all part is together when we say u[i+1] when i=0 it mean u[1]=invlapalce(1/s*laplace(linear part + nonlinear part)
which linear part we have u_xx we put u[0]  so we have diff(u[0]=beta*exp(I*x),xx) 
also non linear part we have A[0]  put u[0] inside each term which conclude u[0] diff(u[0],x) and conjugate(u[0]) at this part this conjugate again make problem becuase function is exponential is not evaluate true 

just one time slowly look at my supervisor code and watch the pdf you will get idea even my code is better but he take out all part and for laplace about that t you said  i just copy the code of supervisor so if it is wrong why worked at there 

@dharr  this time  all structure work pretty but this u[i] remain when substitute why not evaluate the conjugate like paper did, i did but this conjugate  i think make a problem the important part remain which calculating u[i+1] in my file how we can get that

u[0] := beta*exp(x*I);
                     u[0] := beta exp(I x)

for i from 0 to 4 do
    u[i + 1] := invlaplace(1/s*laplace(-diff(u[i], x $ 2)*I + A[i], t, s), s, t);
end do;

@dharr i am not sure is exactly the same or not becuase there is a lot of term like |u|^2 which is |u|^2=u*conjgate(u) and |u|^4=u^2*conjugate(u)^2 also i checked the p[1] is not same but if we devide by 2 is same but in my code is directly give it to me 

Download Dr.D.mw