@janhardo  my deepseek is like that i can't work with it!

about  Bäcklund transformations, Lax pairs i didn't work with them now, but there is more simple work with bilinear form we don't need package even i can get any bilinear form without using this, but for finding auxiliary i have problem  for my last equation when auxiliary is u=u0+ln(f)_x  try this method maybe you can generate a series 

https://www.mapleprimes.com/questions/239878-How-Collect-A-Fraction-Which-Contain
try use this series i am sure they use this to find that kind of auxiliary 

I didn't save last file , nonsense they do dublicate most of questions 

@janhardo i will explain more on  mail send me one please, have another trick which you don't know and maybe you can find general one with this special Ai you have 

@janhardo i like this topic and really is important to me you can find for all by this method ? also if this method is good so you have tt construct for (1+1)D and (2+1)D and (3+1)D also if possible for (4+1) additionally this is the  impotant part of solving some of equation i have  really they  hard  auxiliary which i can't find it , for example this kind i didn't found them even one of them untill now, and please upload the file 

@dharr they say maple can't do that but i told them there is nothing which maple can't but I accepted know by your comment thank you dear Dr.david

@mmcdara  after i finish my work about soliton then i will come to this kind of fluid and i will try use maple for sure, i am sure maple can do that work  too, ofcurse you and Dr.david and moderator and so on are best helper in here 

@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