@janhardo  download the last update of maple file i replaced the F4 tested you have to get F4 by applying the long wave limit on it F4 in maple file

@janhardo i have to finish the long wave limit then i will explain all structure ...

@janhardo I think in this example is like that I have to check in other example too, is complicate a lot 

@dharr i know each steps, but my idea for solving is not good and not fast i will try to hundle by slow way i will try them one by one it take a lot of my time but i will do that, thanks a lot for you 

@dharr i have two ode equation which i used one of them as auxiliary ode and one of them is mine ode which i want to solve it, i use the solution of auxiliary ode  by using another series which contain   solution of auxliary ode,  i can use that table solution which they are solution of auxiliary ode, but i used them to put inside the series to get my solution of ode, i think this time must be clear, and by this solution i use transformation which it will be the solution of pdes in fact.

i know table give me the solution of auxiliary ode but my ode which i want to solve is so different and more complex, which i know if i use the condition it will be zero just i want to tested and see it will be zero or not 

if you watch this file F-P-J-E.mw you will see a series (F) that series is our solution which contain function G(xi) this G(xi) is our solution from table put inside the ode after finding the contant of series in F must be zero.

@dharr  you did somehow about appear jacobicn jacobidn jacobisn and so on i want my solution appear like that can we convert it from trigonometric to that shape? and there is any way to do automatically test all that solution in tht table for ode? becuase if there is not automatically i have to check it one by one by hand for the ode, but important part is that to change it to jacobi form and when m=1 and m=0 like  the paper did two different solution will come out

@dharr i didn't know even we can write jacobi inside equation like paper did, i am working on a method based on jacobi eliptic and i know each step except yours step which is intresting, i have a table which contain 52 solution , 46 are jacobi eliptic and other are weirstrass-elliptic which i can't use use the function at all, i apply for easy odes but i need help there are a lot of fucntion, but i want when i write in paper jacobicn or jacobidn appear in my solution like the paper which i show you in below, this paper  did a good job about written in three shape when we have all type with cn,dn,sn and so on also with m=1, and m=0.
i just didn't do this method about analytic methods,  i don't know how the outcome will be clear more with three type becuase i have to export to latex after the outcome is appear  my coding is a little complex sorry for that  i will put my file in below and link with some picture  also file of table solution 

F-P-J-E.mw

46-solution.mw

paper

@acer  I want 2D after draw 3D which all parameter are fixed, the main parameters are (a,L) L is fixed but (a) change in three different number like (a=0.3,0.5,1) can we do that

@acer 

this is good but i need to complet the work i add some part in below which beside the shape of 3D and 2D which must the result be smaller and smaller in three different of four level of changing parameter the 2D and 3D both importan like the first maple file   and yours which is so clear  there is anyway for for do something like that  

i need the best shape of 2D  while  parameter (a) is changing in different level also for 3D how we do that?

g1_ac-explor.mw

@acer  i want exactly sketch this plot like that which right now you did it, the problem is this i sketch the plot with explor but is not give me this plot, even  i want looking the perfect shape then plotted like yours , do you think 2D plot explor is better or 3D explor option for this plot ?

g1.mw

@dharr  i am stuck at case of non-schrodinger equation which jetnotation not working  i write equation and did some but at there i am stuck, for non schrodinger equation substitution is different is easier but in coding how remove that part which power is >1

non-schrodinger.mw

@acer  this plot is different i ploted explor for 3D in first example but when i ploted and used that parameter is unlike what i want specially 3D of plot but in that paper he did something like 2D plot i need 3D plot but  iam sure there is a physicall trick for this ploting 

@dharr i will keep try using this for new equation which not apply, if i got problem i will notify but the programing is so good i don't think problem come up , thanks a lot you are angel of maple

@dharr  in thus paper i can see we have conjugate but in our i can't see that which i am not sure which one is true perhaps they are true  this is easy pdes for solving and i think if we can hundle this we can do for other too what is your idea?
please also watch the extra note in top comment

p3.mw

@dharr i don't know why i got error and why result  is so different , extra note
when we have |U|^2 i thin we have to use property of complext which say |U|^2=U*U^* where U^* is conjugate

p1.mw