@dharr  in  a lot of paper if focus on it is clear a term must be appear in the first derivative  of (G_t) which must remove that term including the (tau) or any variable with t appear  i changed a lot of other pde  but all of them is like that so something is wrong we do 

F-ode-Fpaper.mw

link

@dharr  in the pde of third  image  which is you solved by tau equal to zero he did term by term if we calculate each term like he did we will figure out where is mistake 

and in paper he did step by step like this 

each equation 3.2 and 3.3 so on  are a term and forget the fractional order 
for example 
M_t= is derivative by (t0 from eq(3.10 and also for other is clear and in eq(3,2) is shown the result if we combine all the term we can find out where is our problem i think our transformation is wrong in somewhere i have other paper too but thus are more clear  , 
i think this is only way to figure out term by term 

@dharr   you always see something which i never can see,  you find a key point i was looking for this key point which no one mentioned ,i have to tested a lot of thing for figure out  the result but this is so important for me  which you did it and i did for the pde1 which  i did like you did but   author without mentioned  he multiply whole equation by V(xi) which make equation integrable  that why maybe  in your maple is not take out  the same 

pde1.mw

after  take some solution , just one problem appear which tau must not be equal to zero becuase B(t) or P(t) is winer process which in stocastic must not be equal to zero  stuck at pdetest 

can you test by the author outcome solution which it will be zero or not based on the my outcome the solution of ode which in pde1 i tested but just tau remain  which we say is must be zero but  when we used plot  must not be zero it will be change something missing in here which is the effect of tau must not be zero 

my openion we did mistake in get ode, without making the tau=0 must  remove all this , i  will put this graph maybe it will make sense 

open this please

explanation

pdetest.mw

@dharr  this is the llink of both of them

first paper

second paper

both of thema are open access, i am stuck at this step 

@dharr  the two first picture is pde 1 and the two other is second , yea  this is true  epsilon^2*t/2, and i think i have to use without u but even i did that is not give me that ode must be this( w*x-beta*t) my outcome are different i dont know why

@dharr  in begin i didnt know which this method is kind of that method have it is so complecated when i was start but becuase i did the Hirota bilinear method is a type of that  i will try to produce a new graph by using that  iteration but  i am sure if i go further  some special finding parameter will come up which i can't handle it   i will ask question like always if that case come up thank you Dr for your help .

i will work on it for clerify all the cases  and also diagrams  .

@dharr this is you solved is from [4-3-1] not [4-2-1] becuae u used three function term ,  when always i try to solve i try to do like the author but when i learn i will do by myself , you did a great job but he used  a different transformation from our i try to do  like yours but  i dont know the result is ot run when i apply for zero, anyway this pde is strange, i try to solve another easyer than this , i  got  whole idea about this method but  i need maybe a week for separate the parts and  my coding really is bad, there is  a lot type of neural method  function but in most general one they use just three kind like [4-2-1] have 66 case for solving pde with different  function  [4-3-1] have 286 without repetition  solution and [4-2-2-1] have more than 1000 function  i dont want all just each one of them i want at least   one of each function  and try to figure out what  plot he will give me , regarding this  i will shared a perfect  file of   which i spend more than a day on it to get the coding and undrestanding is so beutifull to undrestand this , in this file even we can do liek diagram they did in the papers and  i will change the pde in case for countinuos  and i will update  some case about  [4-2-1] which all of them are 66 but i just did 5 or more  , also 1 type of [4-3-1] i hope you help me to  apply for other solution kind becuase they are so important specially the one  which have a different kind of plot and until now no one did it  i will keep contionous on topic until i figure out all the cases how work with it , i dont want to use like the author did i want do better than him and make it generalized, please watch the table in  the layer generating function and watch table carfully 

@dharr  x,y,z,t appear after removing exp  ,  i need your logic for this specially for chossing the function becuase there is a twenty paper  in front of me most of them are use same function , but idea of constructing layer is importan by  some help  as shown in graphs and we can change them by what we want like function of sinh,cosh,sin,cos, exp, anything we want  like combination we can use , i will collect all the function i am try to do it  i did something about layer  tack a look pls

@dharr   stilli dont have any achivement to write but i am keep work on it i will go throgh the heart of topic 

@dharr  i am slow worker but is been while i am focus on it and i want apply for new equation but i dont know how act with the w[1] and w[2] my mean about F(W) i also get another paper which i have to review since i know the effect  of method and really is new i have to apply on the new equation but i dont know how  act for other case i want a lot outcome becuase this topic at least must have 4 or 5 cases i really have to know  about that F(W) function , i think is like that  , since F(W)=W^4+e[2]*W^2+e[0]  one take normal e[2] and e[0[ are not zero is first case , second e[2]=0, e[0]/=0 and third e[0]=0 and e[2]/=0 ,  i want something very fast  for constructing paper now i just have idea and just one case  also i will send you the other paper in the email but that equation have 3 pde   just for idea i will send it,  but again in that equation  i did by my coding  since i have learn your coding , check mail pls for that article and if you can help in here it will be perfect just about 4 cases it will be enough i am working on it too but really i am slow 

@dharr  for the first time i fixed something for you, i have whole idea about topic , when i saw it   i figure out you not apply the condition when we got in eq(3.4) if apply that the  pde will be zero i watched and saw you didn't replaced , something for me is questionable yet how we can apply the other case  i don't know you have whole paper or not i will put here for you to see  it also i got another one which is give us some other solution 

paper

fixed.mw

@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