@Carl Love I executed the code with the initial commands before, it was still same result which is why I tried it without them. I may be doing something wrong, see below:

Download with_codes.mw

@Carl Love 

Thanks for your reply but It seems it is not working for me. See what I get when I tried to get the coeffiecient of u_yy.

Download coeff_D2.mw

@ecterrab 

Thanks, I will look into that.

Most, if not all, of symmetry classifications of such paramerized PDEs are computed directly which turns out to give the general case only. This post will definitely go along way in changing that. Apart of knowing the right way of classifying the symmetries of such paramererized PDEs, one may even obtain a more general symmetry as that in Eq. (7) above.

But one type of such PDEs remain, say  u_t+u^mu_x+u^k=0, which is different from the above since the parameters in this case are powers of the dependent variable. I have been using the procedure explained in the post recent question in Mapleprimes for such PDEs. Kindly confirm if such is valid in this case.

@ecterrab  

Thanks for the promp reply as always. But the commands will not give what I want because the F, P and Q are also functions of the first derivatives of u and v. I have clarified my question below with a simplified Eq (1):

Download coeff_of_DE1.mw

@ecterrab 

Thanks for your detailed exposition. It will be good to repost this answer with the contents visible as promised, I believe some people may be following same or similar approach to mine and use the results (quoting Maple) in their research without verifying first. Just for verification only, I believe the two ways you presented are also valid when the parameters are power of the unknowns? E.g.

pde:=u_t+u^mu_x+u^k=0

@Preben Alsholm  Yes, you nailed it! The case m=0 not considered by map(pdsolve, [res2], parameters = {m}) is what caused the "inconsistency warning".  This shows that the result given by map(.....) is still correct but INCOMPLETE! This will definitely be a problem when a lot of parameters are involved, hope the gurus at Maplesoft will see to this. Thanks once again @Preben Alsholm for this alternative. 

@Preben Alsholm  I am actually interested in obtaining the Symmetry Generators so as to use them for a different analysis. If you see the file I attached, the generators were given at the end of the execution even after the "system is inconsistent warning". My concern is whether the warning has an effect on the result or not, if it does then how to fix it. Anyway, your detailed input is dully appreciated. I have learnt one or two things from it.

@tomleslie 

I actually want to obtain the Symmetry Generators to use them for a different analysis and not (really) for the solutions. Anyway, thanks for your time and input.

@Markiyan Hirnyk 

Thanks for the help, that is exactly what I need for now.

@ecterrab 

Thanks for your timely answer, the detailed explanations are well appreciated. After fixing that aspect, I  encountered the following problems:

1. All cases (eg, k=m=n which is pde2) are not considered as can be seen in eq. (4) of the attached file, how can I rectify this automatically?

2. What did I do wrong on pde2 that leads to "system is inconsistent" in eq. (9)?

3. I beleive the conditions that appeared in '&where[...]' govern the casewise results obtained, if that is correct, then there seems to be a contradiction. For instance in eq. (8) , we have (after results for k=-1)

4. How can I classify pde3 (eq. (10)) for the functions a(t), b(t), c(t) and d(t) just as is done for parameters?

Thanks

sample2.mw