@janhardo  thank you john you did a perfect job

@dharr @janhardo @mmcdara  thanks for all of you, all of you made my day  and have a big part of my PDE solution i am very greatfull to have all of you in this website. proud of all of you 

@dharr How i can tell it? is that like this ::n>0,  How reach this point i am shock when i saw this and when i saw your answer i got duble shock ...thank you so much dear Dr. David

@mmcdara  in john code we have this  for f[4]

How they remove is multiply by something or what? is so confusing for me i didn't work with such series with combinations but i have too , also i used your code and for sure i will try to upgrad it i can't do more with it but i will make merg with other code for getting the best result for my solution.

@mmcdara  thank you and @janhardo  this is emazing i can't beliave that which i found this , i will try to get solve the pde now , just try to change your version of maple i hope the B[i,j] not make any problem in coding but today you made my day i will check them later for solution thank you so much....

@janhardo  you did a good job i check for f[2] and f[4] and half of f[6] by hand determined each term one by one all true but the fraction number are extra How remove thus fractional number beside each term? i know in series is determine this number but i don't know why they remove it !

@dharr you did the limit so pretty just one step remain, and equation (11) is true i find exactly same!, i need to get the series without series we can't go further in all paper they mention this which from N-soliton reach the M-Lump by applying this , what they see which we can't see 

in your paper which linked mention this note too in below of (22)

for w(i)

m-lump.mw

if needed other paper please mention to upload more and more 

@mmcdara i just mention the second restart for know how the series work is strange series and the second series is making like that  but contain a different structure i want to make that series 

@mmcdara  we have two series the second series which contain product multiplier  we need that series watch lump you will see, but instead of N we must put 2M which m is number of lump ,for F[N]=F[2M] so in  series we have two define b[12] which we have it from N soliton is a[12] after that  in a[12] we have two take limit from a[12] when k[i]->0 then we get B[12] and then we can build all B[12] in 1 and 2 lump and 3 lump  i just need that series which contain product  and if possible apply k[i]->0 in a[12]=B[12] 

@mmcdara  why in function you just replace b[12] where i should add the b[13] and b[23] where  add code for substitute other b[ij] substitute 

@mmcdara ...........................

@mmcdara  thank you dear

@nm  that is so good now i can calculated easily  thanks so much

@nm thank you so much 

@nm the question are so different even if you watch this taged question they write dublicated where is this question i don't know