i did seperating but but is seems is not correct what is mistake in here?

issue1.mw

in here  for jacobieliptic i got two lambda[0] same as paper did but in second one is different and is true make my ode be zero, but is so different from paper 

test-Dr.D.mw

In here i replaced but i don't know why still the D[1](f)(x, y, 0, t) is remain in my function in equation eqt1, beside this my function contain imaginary part we can plot this or we have to remove that somehow?

eval.mw

in this method i don't know in most of short equation i try to find the parameter but is just evaluating and nothing come up i don't know my way is wrong or write but i think i am right  but parameter not coming out, beside this in this equation give  me a warning regarding the parameters which say number of solution is more than 100 and dint show me that , how i can find the solution better than this?

f-p-.mw

Before at most a year i asked about this applying long wave limit which is coming from some kind of series which i am not sure to how get this result from the series but i provide just the two function of series for appyting the long wave limit and then we can generalized to N value of them, i asked to Ai too he give me a good explanation and somehow he did programing but  i am not cool with programing of Ai,  i  am looking for result eq14 and eq 20 , i have a series for eq(12) N=2 and for other N too but by applying long wave limit it is become to eq(14) and then F[4] becone to eq(20) i want that result by don't have any idea how reach it  

Long-wave-limit-testing.mw

Ai-result.mw

update F4