@sand15  when i run it it take a lot of time visualization is perfect more than matlab even, How about the 3D we can have something like that , but be a little fast work too is will be better

@janhardo  i did this but result is different

@janhardo  i need just one step no more

@janhardo  i need evaluate |u|^2 but by code what code we have to use for get the same result?

@sand15 something wrong in my changing pdes which is related to complex number and i don't have idea about that kind of substitution which work automatically 

@dharr  i try another method but you did the same as paper did , i am looking for a methods for finding this kind of pdes i will try more and more  thanks a lot 

@janhardo i need solving not writing 

@dharr  i know is confusing becuase this topic  have a lot kind of solution of pde, Soliton=5 type, lump=3 type, breather=2 type, interaction between them also have at least 8 type each on of them the solution is change, but i am sure if for the first two one is correct and without doing substitution is give me zero it  will be  done , if you watch carfully you will see after the first solution make pde be zero in (pdetest(eq19, pde)) then when N=2 start we look for second solution  if that solution make our pde be zero then we say that our substitution is true ,  but how find that condition which make our pdes be zero i am sure is related with that part becuase if you want be sure set all of the function of (t) be one, you will see  the second solution is satisfy pdes

@dharr i know where is problem but i don't know how find the correct one watch this picture

i did this change (red part) this red part is not true is not work if do this change it work just for first pde for other is not true, but i know there is a condition with one  exchange (we look for that true exchange) and substitute it can be any exchanging it will work for all so how i find that i will take another shot in below mw file

another-c.mw

@dharr  i solved one another before he didn't make any problem  and without this issue it  give me zero, maybe i am in mistake i trust your way about the last pde which make it to zero by substituting and really it work but know about this which not give it to me zero i am in dubt about that i think  without replacing parameter and function must give me zero, so in here i will sure which i did a mistake and replacing not work is my openion 

in my pde  i did a substitution  if you watch  which is  alpha(t)=beta(t) i did that by myself becuase for finding R i need to do something like that, if i don't do this substitution is not give me zero in first pde but also this substitution must be true for second time, if not work for second so we figure out we did mistake at there at that substitution, i don't know how act with that substitution do you have any idea  about that at least one function of (t) remain in pde  which worked for both pde, there is a lot of pde which if i can find this condition  for them i will be super work

really need that changing of function also we can change them to a constant but at least one of them remain and make our two step pde be zero i am sure if untill second one be zero it will work for other type too, i hope find this i will mark in red color 

C-find.mw

@dharr in here why when i test without substittue parameter is not give me zero but when i do substitute is give me zero?

really is problem how this is possible?

problem.mw

@dharr   thanks  i will do and go to solve a lot of them  by this way, becuase by number is zero so it mean we did a true way thanks a lot 

@dharr  i try to evaluate but is failed 

p-test.mw

@C_R  thank you i didn't see it before , but is so usfull 

@dharr i don't know when i will learn this, Every time I think about what I would have done without your guidance, I can’t find the words to thank you properly. My dear Dr. David, I truly owe you a lot.