@mmcdara  they use matlab because i think they have a lot of iteration and they use special pc 

this is so good topic , i liked, but this is not apply for all function i try to solve them more but this method not good for finding all and maybe i am wrong about that i will update some pde here if you can finding auxiliary function u=ln(f)_x it will be soo good , if you need any help you can count on me for finish this invistigate 

U.mw

@mmcdara  just one another step if you do for me i am be thankfull so much, your explanation are so good but in fact i have to do by myself with a lot example until learn better than you  but i don't have enoght time like a beginner  start this topic ofcurse i will back to this topic but when i have time without stress, at  PhD course  time is the important, anyway 

you did one time before i have that code  and i saved about (M+1/G') and you make a good system of coeficent  like list all of phi coeficent  can you make a system of this phi but first replace the S,S1 then substitute and solve system for finding parameter ? like in picture i need that phi but first i have to replace S and S1 ,

something like that 

@mmcdara i think you know how do this kind of technique, do you have anything new about this kind of solution for pde new method like that?

also something is missing i want be sure about that in last step you did there is a G(xi) and  diff(G(xi),xi)   which is i think have to replace by taking derivative from S diff(S,xi) then substitute becuase some part of coeficent contain diff(G(xi),xi) and G(xi) after that we can make a sequence of all coificent of W , we can find a parameter like he did? i did some change i hope they are correct

find-parameter_2_mmcdara.mw

@dharr is give me answer but is not true! This is so different I have to generate system for all kind of finding parameter this is one of them if you need I will upload (2+1) but is so different from this, in other problem I use different way of billinear 

@dharr in last code which i solved it have zero, becuase of that i did! i don't know my parameter is strange i think is wrong like that becuase u is number and my function must have exponential and some other term which construct the soliton by it ...

@dharr I copied the equation at my other file because of that I didn't notice that thanks dr

@dharr 

Sorry for my late response. I was searching for papers related to this issue in my investigation. I have collected many papers, but none seem to provide an explanation—or perhaps I just haven't noticed the relevant details. If any of them could be helpful for the investigation, I will send them to you via email, as I can't upload PDFs here.

also my opinion is this because of that they do this when I try denominator without having K[s] my function is singular and not give me my graph even when I change the parameter ,

additionally, in paicewise function we set j>=3 when we use series of F_3  in some of thus paper i send to you in linchaue they set j>=3 one time and another time j>=5 when they use five it mean they use sereis of F_5 after apply long wave limit to it which still i don't know how reach that but i used as known function 

Thank you so much, my favorite doctor!

@mmcdara  before a long time ago you solved one example it is same please check this and you will get the notion of topic is easy i think but need a good codinger like you

please check this link

https://www.mapleprimes.com/questions/239878-How-Collect-A-Fraction-Which-Contain

@mmcdara i am thankfull for your help, maybe my question is bad becuase i have to tag some some example with it this is my openion which we have to find R[2],R[1],R[0]  in  most of article i seen they use R diff((ln(f),x$2-1) or R diff((ln(f),x$2-1)+m which m  is unkown i have to work more on it then i will requestion this, but becuase of example is so complicate i just mention the exact work but this time i will tag some example too with it, last time you solved one example like that let me check it to find it in my questions

@mmcdara just put file of maple without showing up the mw.file, did you plot is same example before I try to use your code and mine to see have any different at end or not because by your way I can plot all by mine i can plot a few , also w[1] w[2] i think automatically calculated because is depends of parameters 

i try to plot even with calculate w[1] but still not plot 

line-plot.mw

@mmcdara i use explore but is so slow and i can't manage all parameter 
 

why always say be clear is not my fault my question is hard

@mmcdara this is good but the most importan part is where i choose parameter for make function  not be singular problem is parameters

@mmcdara i invistigate a lot becuase of that i didn't response soon
i solved a lot example and if needed i will upload the target of this finding if mentioned, about this kind finding in begin i was so happy to use this way for finding (x,y,z) but in some example which i get my result by use the old way i try to use yours too but the result is so different why? 
in begin i try for 3-dimesion  which i didn't solved yet but result is a little bit strange becuase of that i try a solved one already
i will upload the mine way and your way and watch the different !

true-one-By-me.mw

wronge-one-by_your_trail-mcdara.mw

@nm is hard for me to learn how use this notepad++ i will do by classic way...