@dharr in fact i am looking forward to find a generation function and use a loop for test that generation function for finding solution for ode, if possible i am sure it is possible even if maple can't find them i don't have knowledge to write down the code but i have idea , becuase i saw a lot of ode which no any mathematical program can find but they tested manually by hand but if we do by generation function and take out that function which make ode zero, i will post a new question about this topic ofcurse we can start by small ode and small generation function 

@dharr all of that function i try more than 3 kind all of them make a problem and when i found parameter the parameter set of parameter are so few and didn't give me answer for this equation i think this way is not usefull for getting solution i will look for another equation, thank you dear Dr

@dharr i found he did this part 

@dharr in fact, this is first time i solve this  new equation, the other equation the monomial of them is not to much but in here is more than 10 , i learned this trick from another paper, which have a lot term he just say take coeficcent of thus, i say maybe this trick give me answer , also my other problem of mine i don't want find all parameter just thus which contain in (f), and when i do that it not found and just runing , i am looking for some pretty solution of this pde and really i don't know the true idea behind of this exactly,i want choose thus parameter which make my PDE zero,  also in file have two H function please delete the second one which have one derivative in right hand side

S11-Dr.D.mw

@dharr thank you so much ,

@dharr if i am  automatically not get explicit answer i have to make them which one of them which this take a time, no problem thanks so much 

@dharr Every time I read your answer to my question, it brightens my day.
 

@janhardo thank you you did a great job thank you so much

@dharr i don't know where is should add print function u in loop, becuase i have to latex the outcome of u i have do it by hand  but if loop do it it will be amazing, also i need just thus parameter which contain in f (L2), is not different if have thus extra parameter but i don't know why my code not answer is not work when i write solve (L2,{a[1]-a[11]), also if have explicit option it will be great
thanks a lot 

trail-pdetest1.mw

@dharr So you say first i have to check in F1, then substitute in H then pde, that is also true, but i asked a new question related this a hour before, i try  some of this variable all of them not make my pde to zero but some of them do, i want seperate them at there , also if possible in ans[] just find that parameter which belong to our auxiliary function in L2

@janhardo  like that don't have problem but i have to change it by hand all of thus F to f

@dharr  i get exactly bilinear form of that is that like i say need the derivative and i found it , but why when i replace my parameter is not  give me pdetest zero, i try to find parameter a[1]-a[11] alone without other parameter , but didn't give me answer like paper did it , you are so good at finding parameter can you check it please 

Download test.mw

@janhardo can you change the letter F to f (capital to small) becuase i have to copy past equation i  needed also for G to g

@janhardo you answer all question you are going to modify your Ai i like that , just last my question he can't answer thank you it work i have to check it then

@dharr let me give you a hint maybe already you know this, but lineaer part of pde is the same of bilinear equation, and 5 month before macdara write a program for me about how open this derivative and it is totally corect for (1+1) dimension when it is (x,t) but for (x,y,t) and (x,y,z,t) i don't know why not working , i want to check that if i open bilinear equation is the same as linear part or just the shape of bilinear form it is , i will explain more if you needed , 

i though equation 25 is linear part of my pde, the bilinear form it is i am sure %100 percent, but when i open bilinear equation it is equal to linear part or not i am not sure, i have to open by hirota derivstive in here i try it but if watch and make it for 3+1 dimension the prcecure we will be sure about that it is bilinear form or not 

also i check the result i don't know something must be mistake otherwise your code are working so good 

Download test-Blinear.mw

Download system-pdetest.mw