@dharr  you are right is not clear so much i have a lot of example i will put here more, and in fact i am stuck is this kind of solution there is some people very well do this definition and really i want to do too, if i apply this i can solve a lot of equation of PDE , if i found the f[N] in any N i can find N soliton , sorry for late i have them in hard copy i downlaod them again ... i hope help me for finding this is so important for me

@dharr  so i watch the different between mine and yours is just there in this line i didn't put : ->eq6 := eval(L4, {t^2 = Z, x^2 = X, y^2 = Y}) is this different so if i put this in last of each equation is remove the issue ?

@dharr it is work thank you dear Dr

@mmcdara so good but is so high level 

@acer  it help me a lot is big help thank you so much 

@acer  the plot of the countor is same is like yours but density is different  i don't know How he get the density the countor in matlab is not like that is so different but  i need all of thus plots i don't know why density is so different from this

this picture is another function in that paper 

@acer  i forget to add this picture , this is middle one is density also i want countor plot i don't have the code for countor plot in maple

@dharr I didn't delete thus post moderator did,thank you so much 

@dharr in here  i can't distribute x*t to another variable i have a lot of this kind which they are different but i need go one one by one 

Download replacing.mw

@janhardo a am looking for it but  a long time ago people find this with maple and mathematica too

@mmcdara i have to invistigate more then i will repost this in that paper i saw this, he didn't explain much but it is intresting for me we can plot polar of such function i will invistigate more and more , also your code are so high level i can't involve it  and change the thing 

@dharr So becuase of that didn't give me any outcome Got  it thank you dear Dr

@dharr your code not run i don't now why not run, so i used my own code but i add your comment and is Unbelievable i get my solution by using your word just lhs to equation 8 ,  this is my fist time i solved somthing like that i don't know how say thank you, this is easy one i prepare my self for further please in next up come help me too thank you so much 

@dharr

 N-soliton1.mw

@dharr thanks dear Dr. but why don't go further i will stuck i am sure i did that by your code untill here is so hard for me becuase strange thing will coming up for collecting