@dharr  i explain some more  in  after your worksheet ,  you already done but pdetest remain  i am not sure it is satisfy or not 

P5-pde.mw

@dharr  until solution is good we don't have problem, but the idea for reaching the final result is wrong, we have to change the solution  by replacing in eq(3.1) and eq(3.2) which it will be the solution of eq(1.3) , i am busy with it but something is missing  in my coding which i am keep work on it, so idea we have to cahnge the solution of eq(3.13) by eq(3.2) and eq(3.1) directly test in eq(1.3), when we got one solution of that shape then we can focus construct the other solutuin becuase there is 18 solution he got by that table i can upadte the other solutin if needed? dont worry about if your solution not be the same as author did  becuase sometime it is happen which have a lot different  but also is solution...

@dharr  you did a great job is ok if your result is different from him that is no matter the idea must be like this that solution you get must be the solution of ode first  eq(3.5) based on thus changing variable also that epsilon you can mentioned be one,  that solution you get arctan(#) must be solution of eq(3.5) then  replaced eq(3.1) must be solution of  eq(1.3) which is pde ,  also he metion a table 2 after eq(3.11) which i update here , i am not good with this transformation  eq(3.6) but when you get the solution the solution must satisfy  and  in eq(3.13) is a solution of eq(3.7) then he apply eq(3.6) to get  function (u(xi))  then he substitute in eq(3.1) to get final answer  of pde beside  your coding is work so good but i am not familiar with some coding in replacement and why you replace w(xi) by W i am not sure about that quadratic using why he use that even is  a special kind of analytical method which this is so different from other i am intrested so much  if apply to get  solution of pde as he mention it will be something very different also you can use your coding and even update the steps he did it 

paper

if need any help let me know i am work on it  but some replacment make a problem for me i can't handle it , also dont   use equation of him like eq(3.7) as you suppose maybe he is wrong use yours 

@dharr  

D1.mw

@dharr  as i said until the  eq (3.5) is very clear for me but next to that is unclear just two variable are different  r  and c which i always use w and v i changed to that but this is not gonna help anything is just about idea and this is new in fact i changed but  i dont think it help 

@dharr  i use mine variable but result is same untill that ode is easy but after that i can reach out how he get solution really is  hard to undrestand by taking that integral  eq(3.7) and eq(3.9) thus are hard, and it is new a few people know that  and for me is first time to see this if i can figure out i can publish a lot papers by that but really is not easy to undrestand this part for me at least 

@acer  it is a simple code but i dont remember where i saved  it is like when we have a hyperbolic solution the same solution we change to trigonometric solution they are equal  but at same time different , Dr.David did that but i search a lot for code but didnt found it....

@dharr  i will try to apply for more pdes by this method, the important part is this you always do the right thing whick make the pde equal to zero your mind is magical , i will work on it to construct the best paper by this  i hope no problem come up  and i will search for suitable pde, thanks a milion times.

@dharr  with you nothing is imposible i will try to use this for a lot of pde i hope no problem came up, also i try to use for another  system  again a problem came up why coding not work with my hand? can you take a look and see the problem foor this system? is like before but i dont know what is issue 

f-2s.mw

@dharr  i try to reduce the pde to one and i change the problem and change the code base on your coding, i did my best but the outcome not give me zero and i can't find the issues

F6.mw

@dharr i am sleepy and topic is hot, already use sol1 without that subs in sol2 is again make pde zero, so we dont need that always the parameters are different some of them this is happen always and the important part is the pde be zero by that finding we did, do you think we can do this method for other pde or even the schrodinger equation  ?  do you have any idea? my idea is that for schrodinger that xi=(P+Q)*exp(i*(#)) and then remove imaginary part or finding the some condition in imaginary part or ignoring, i remember once you did this substitution for finding stability maybe we can use that for finding  ? tommorow i will try for other pde and i will try for schrodinger equation i hoe i found a treasure  in this diging 

stability

@dharr i am in rush to see it , if this is happen and work really is gonna be something really new 

@dharr let me explain a little bit more, this paper is from 2006 and i didn't see any one use this method becuase really is not easy to figure out , author explain in two way the other is too easy and i know, but this is explicity find the solution without any auxiliary equation is just substituting and finding, i am not sure this way is possible to find the solution of pde or not but  as i see you did a great job and already find thus parameter so it can be possible, i saw that  author use a different (xi) from yours i did a good explaining the maplefile too and i will put here the DOi too, also there is another question for me is come up the K[1](y) and K[2](t0 in (xi) or even in function if they be function of y like sin(y) sinh(y) or k2[t] be sin(t) the figure will be intresting, i already did the testing of all the case of odes in case needed just mention becuase in maple file i just put one subcase from 4 cases , watch equation (27) must be solution of our pdes which phi and xi are clear as i mention , but he use another  (10) i used the (1) 

paper

F3.mw

@dharr  is good idea but already i did some change variable  by that point  i get this equation maybe is not suitable like that if thus fractional  appear

@janhardo 

p1.mw

p2.mw