@acer i want update my question to get answer if i add no one see becuase of this i add a new question and you mention my tag a dublicate question what i do is your false let me ask my question in anyway 

@acer  i delete questions becuase i update with new detail , john did but is not my answer, this question is more specific and shorter

@janhardo  i am looking for finding each part, not use them

@janhardo i have to make the progress automatic i need to find each one of them seperatly and used , you use line and make the graph exactly but i need to find the line

@dharr thank you Dctor 

@dharr  dear dctor there i get the first section but how about the second part my mean in theta i must change it to i can do it by hand but how apply something like you did i try to use it same method but in here is not give me answer after simplify too as mentioned in picture xi will change to theta i can do by hand but how about coding?

long-wave-limit.mw

@dharr  i didn't thought about simplify i get my result thank you dctor how you now this kind of think saved me again thank you dctor

@mmcdara i think there is a key point, becuase of that, untill know i reach two paper which i can't find a[12] in auto.mw becuse in second part (p2a) why we can't find a[12] what the problem find a[12] is end of this , but why we can't ?we did something mistake , must be a way for finding i can't leave it like that, all the paper didn't show step most show just  result becuase they are too long ,here is a place which i can get a best help , in mapleprime a mind exist which if i search all around world i can't find it and thank you so much you did a great job , i think our method is better and there is no mistake just something exist we can't see it to find a[12] i want see that , this is a questions and  maybe a challenge for   a genuis like you 

@janhardo i upload the mw file for maccdara in top  ,we can't find a[12] for that and all thing is set up and true just our u and w(i)(t) is not same as paper did becuase of that in p2a we have 19 exponential, we must have just 3 of them something is wronge there

@mmcdara  the problem are  w(t) or u they not the same i don't know why, otherwise maple can't solve this  becuse there is no any error in steps

@mmcdara  i have a demand if possible i want apply this  series for finding a[12] in my last equation which we can't find out becuase this sereis in our method is not same as paper did , if you watch our way for finding is so good for some of them which don't have the constant in u(x,t)  but when we reach out the constant  i think it will be different but my method not find thus kind of trail is just for R* ln(f)_[x$#)  

there is two file auto which Dr.david try and  is so close to find it but i don't know why not succes my openion is this which our trail is function is not same as paper did it means (u(x,t)) is  different, but if you use your way and figure out as paper did if trail is same then a[12] must come out  

a[12]-pde.mw

auto.mw

@janhardo how reach that ?I want use this method in  solving last problem 

@janhardo  i will try do another post which maybe related to this one

@janhardo  my openion is just this remain the trail function is wrong, i have to look for another way for finding i have to try finding series, Dr.David did a great job about finding this parameter but didn't give any outcome so there is must be another way  

@janhardo i need find the a[12] step by step not copy past