I am trying to calculate the stability of my solution using this integral test:

U = 1/2 * ∫ u(x,t)^2 dx

Then I want to compute the derivative with respect to epsilon and check if the result is greater than zero or less than zero.

I tried to do it in Maple but it is not working correctly.

Also, I want to substitute random numbers for the parameters to test stability. I prefer to use simple integer values like 1, 2, 3, etc., not decimal numbers. When I try random values, sometimes the result does not evaluate or gives complicated output.

S-test.mw

is been a while i work on it but i can't figure out where is problem and even my solution is so far from it when numerically i tested , i got same outcome as the paper did maybe is  long but it is same and maybe have some typical different but they are same , the problem in here is that which when i substitue is not my answer i don't know where is my mistake ?

pde-te.mw

f18.mw

f19.mw

this transforamtion including two function which i try to do, but my result is so different and even is not near i did like the author mention but i don't know how reach that outcome, the importan part is the equation 2.7

s1.mw

in here i want to apply this method for finding my parameter but is a special kind of substituion and i don't know how hundle this kind  and find the parameters i did some part but i didn't reach the target 

f-p-second.mw

almost i did all the case but some case i determined in red color are not satisfy what is problem of them and how i can apply the case 47-52, beside this i changed the ode in eq(15) i didn't write rho parameter  is make any problem?

ode-17.mw