@dharr this is novel methods and I am chosen to apply for one of the equation I will work on it by the last ode which work. Thanks a lot 

about long wave limit, I know every structure but is a little bit long It contain two maple file except some extra function which need more maple file I will send you after I compact and write a good explanation, I know every structure and I know they do by two way in first we will start by my last equation is necessary to find out this step my package is missing something with out this .

@dharr it is work but i don't know why is not fast as i want , i dont need all parameter so this must make the procudure faster but i don't know if i have 7 equation so must be easy for finding 7 parameter the main parameter is A[0]-A[2] and B[0]-B[2] and if add one another like w it will be good ,  i think it will be wrong if i find lambda att all becuase in some pace in future steps i have option for lambda like testing ode solution inside radical for example sometime we say lambda[2]>0 or<0 
dear Dr did you see my last question about long wave limit? really i am in bad situation i add some explanation if you watch you will figure out i am sure about that ?

i have to test all of thus

tt1.mw

@janhardo  is not related to bilinear form is so different this is another topic just apply change F2 to eq 14 by that information in pdf

@janhardo  is not even close to our  solution, don't use series like that in begin start with F2 as i give it to you then apply to long wave limit then you have to get eq14 also for F4 you have to get eq20, so you have to use this two function begin  and do  that operation i explained in top as Ai did find each term seperatly  like A[12]=1and some term will be zero  watch the step   i showed in picture in top tell your Ai to get the result by thus explanation if it can

@janhardo  we have a series to construct them i have tht series you constructed last time, but in some Function like F5 and F3 i have to apply this long wave limit if by using F2 i give it to you you reach the eq(14) and by F4 you reach eq(20) then i will give you other Function like i F3 and F5 to apply by long wave limit untill  F5 the long wave limit exist but i need to apply to finded just focus on how change F2 to equation 14 and F4 to equation 20

@janhardo  let me see it  what you did , in this topic just this step remain which i am very intrested to do

@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