this is my first time something like that   coming up my equation after taking integral exponential coming up why?

g1.mw

the series is so complicated but have a strange pattern if you watch the index of parameter  they are not repeated 

How i can get FN from N-soliton to FN for M-lump by applying long wave method and using limit How we can get the series of lump , there is some example for nowing how lump work like f[2] for 1 lump and f[4] for two lump and f[6] for 3 lump i, and also in last of work i showed the series of for n soliton which we can change it to m-lump  but i don't know how work and a[12] will change to b[12] by applying long wave method

m-lump.mw

I did some example to change them but i didn't get the same result as book did it and i try to figure out by hand i get another result i know all of them are true but polar is for making the simple shap for ploting so How i can get the simple shape and if possible How do step by step like using totur we have for polar or not? 

Download polar.mw

It been a while i try to figure out How they find dispersion parameter and phase shift i figure out how find dispersion in some of pde but some of them is not give me even dispresion parameter i don't know they wrong or i am , but for finding phase shift there is three cenarios, when we change pde to bilinear form we have linear term in bilinear form so after substitute in linear term f bilinear form we can get dispersion parameter which is a parameter beside (t) also we can generalized for all of solution by changing the number of parameter as mention in the paper, but for phase shift parameter i don't know how find it i must substitute our solution in linear term or whole  bilinear form of in first pde linear term i try all  but i don't know what is i did mistake the paper say put in pde but i think he mention the the bilinear form i did all part for one soliton is w[1] for 2soliton is w[2] file i just want find parameter a[12] in paper for 2-soliton eq(19)  then i will find for other just i need to find one of them, thanks for any help  in this topic .