@mmcdara your idea for solving questions is emazing i like that, the idea of get solution is so simple but i couldn't get how? and i want use this formula for other problem but i should start with simple one i don't know why i can't get same result as i show in below in picture they don't use tanh[#] instead they use cos[#] and do substitution even when i use cos[#] when i take derivate two time i can't get same result soemthing is missing i can't see but if we use eval by taking U(W) we must get same result but i can't ,this method called sine-Gordon expansion which a lot of people used 

@nm  How he got thus equations? the equations build by this techniques 

@janhardo  How i can contact to them ?
really i need some expert for improve my physic notion?
 AndreiD.Polyanin or
AlexeiI.Zhurov

@janhardo i am work on it and i write my desertation on this topic, i succed to achieve my code with help of mapleprime ofcurse  and now  iam work on this topic more and more is like sea is never end but i need to construct new code and new technique i am search and work on it still 

@janhardo  is a little bit complex for someone out of this topic after the transformation you should seperate real and imaginary part then solve it  by technique

@janhardo  i don't know how apply D(U) on pde this is problem, i solved the problem by other way but i need this way too

@sand15 i need quality of graph with best effect shown.

@acer  i need plot thus graph but quality is more importan in here i don't need caption but i don't know how add legend ! 
i need eps. quality as in matlab with full quality like this 

in this problem i don't have other program i saw one or 2 other build a program for such graph my graph in maple is not like them but effect are same they did like 2D plot and 3D plot with effect and without effect  i ndid too but in maple  withoud 2D effect,  really  i am not sure what i should do to get best view of graph 

@mmcdara  you did already thank you for your help and response

@mmcdara  i know the ode will be zero but is wrong becuase is a number my function must contain xi at end that is becuase of e[-1] and e[0] and e[1] if e[0]=0 it ok but e[-1] and e[1] one of them must not be zero  for finding solution when we say 
(m+G'/G)=phi if you watch the result you will get G(xi)^4 this is extra in our system G(xi) must remove, is like (1+1/G') method you did before , some thing like this must remain 

@Carl Love  thank you sir i got it .

@acer  you know very importan thing, i am looking for this 1D a day  but i didn't find it  your code is mapple inpute also there is just 2D inpute 2D math i can't see 1D

@acer  now i undrestand lprint too, but is so hard to know this stuff is emazing  i have this problem most of time . thank you so much .

@mmcdara  also i mentioned the solution diff(G(xi),xi)=# in our solution i must substitute this in my solution in last formula we have just diff(G(xi),xi) but in this paper we he have G(xi) too which is a solution of this ode it is clear in paper  writed already  

@mmcdara  also don't find all parameter becuase in this ode part we have condition i founded before but becuase is not neccesary i didn't mentioned please just find thus parameter in paper mentioned V and sigma are condition i found it  in first part which i transfrom the PDE to ODE i get it from imaginary part  so i don't want make confusing for you becuase of this i didn't but i will mention the condition 

condition.mw