@Scot Gould i know you don't answer my question and you know them but  my questions are not same they mention in tag dublicate if i online i will remove dublicate but at that time even i don't know they taged dublicated, i just see notification which you answered!  i didn't delete thus which you answer and really it will be so good if you answer  watch even this post in top, it is not dublicated question but they mention is dublicated is not my false and sometime when in 24 hour i didn't get my answer i will delete and again asked same question but with more detail and they say you don't have to do that , and this act is just seeking for get answer in short time with update detail ,even in this post i try to solve another example but needed time for collecting information

@janhardo How find this line? How find eq(11&12)? How Find v[x]&v[y] this is important part, if i find in one case i will do it for other just need this each part seperatly 

@janhardo i delete the question becuase they didn't  let me ask another one with the same topic, yes i think there is a lot people who know about that i don't want go in this convesation , you did and it is correct the graph is exactly what i want but importan thing is this How we reach this result there is a 1000 equation we need find for them at there we don't have solution for watching we need finding, i need a way for finding  each part and structure step by step ,

@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