@janhardo a am looking for it but  a long time ago people find this with maple and mathematica too

@mmcdara i have to invistigate more then i will repost this in that paper i saw this, he didn't explain much but it is intresting for me we can plot polar of such function i will invistigate more and more , also your code are so high level i can't involve it  and change the thing 

@dharr So becuase of that didn't give me any outcome Got  it thank you dear Dr

@dharr your code not run i don't now why not run, so i used my own code but i add your comment and is Unbelievable i get my solution by using your word just lhs to equation 8 ,  this is my fist time i solved somthing like that i don't know how say thank you, this is easy one i prepare my self for further please in next up come help me too thank you so much 

@dharr

 N-soliton1.mw

@dharr thanks dear Dr. but why don't go further i will stuck i am sure i did that by your code untill here is so hard for me becuase strange thing will coming up for collecting 

@dharr i wish i could i just know what i show it in here a simple trick have which i can't figure out 

@dharr i am still work on that you did , but this is different from that, when that you did before is for that function contain x and t two parameter and you did great job at there, but in here this is another method your outcome  is wrong, let me explain if you watch our function just A[0] is constant other are zero so our solution is just constant is not possible must other parameter like A[1],A[2],B[1],B[2] at leas one of them  have to not  be zero as they did in most paper, nowday i am stuck to much ... if watch the picture in below i mention some for comment of maccdara you will get full notion.

@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.