@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

hidden_layer.mw

@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

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

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@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  

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@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 

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