@acer this code is emazing specialy when we do change variable by range of  parameter, that you did is exactly my mean but the picture i don't know why is not so clear and name of them is real or imaginary or absolute or countour or density i want search for each graph and like you did the change parameter for each one of graph seperatly , and if possible can we tell the maple search for wave graph or kink or dark and bright graph , i want graph seperatly not  all together i hope you do it because already you did it but need detail thank you so much and sorry for late answering.

i always use this code and is really painfull and wasting a lot of time to find each one seperatly and each time change parameter and again watch plot watch we have is wasting time a lot i want something like you did with exploring but i don't know how do it please watch the code and make it to exploring if possible, also i want conversation language to matlab of last function if possible

i am looking for a graph like that in below and also this graph is construct by matlab by maple is big help for sketch them let me give you some example

@acer  I want someone plot the solution of this kind function and explain the phase and magnitude and how paramter effect the plots , this function is hard one for plotting but there is any code for giving parameter plotting automatically I need a code for parameter search automatically and look for my graph there is anything like that 

@acer If I don't have this perfect group in MaplePrimes, really, I was quit a long time ago.
thank you so much sir this is exactly what i was stuck ,every thing is done and in test i am stuck thank you again and again i am glad so much for this really is new thing for me  and i owe you .

@dharr  thank you for you help with your code, i am intresting in your code always, unfortunately still i didn't learn how i get all equation with writting program but i will do my try, yea i copy and past equation i did't have a choice for now , i found mistake after a short rest and seen your answer , the mistake is in beggin in (2W) must replace lambda .
are you best Dr .

@acer  thanks sir

@mmcdara in fact i am not sure i am right or not i am stuck at solve and i use one of your code for replacing G'/G in previouse of your work, and i don't know it is true or not , becuase of that i say please finish the work maybe i am wrong i don't have solution in fact i want apply this method for this equation for first time and i can't replacing i am not sure of this solution, so please go ahead i need to see what will happen and i must find parameter no matter is complex or not and is not needed to find all parameter just 4 or 5 it will be enough i will use thus parameter in PDE equation and after that i will use it for plot of solution, if the work finish for sure i will send you total program so please help me, maybe becuase i am solved equation in wrong the solution will not up come so really i am waiting for your response.

after we find parameter we will choose the arbitrary case and replace in ode solution and put ode solution in ode  equation  must be zero this is in my mind i watched your code but becuase my low skill i can't add things so please finish up .  for any more question please don't hesitate.

and i thought i was right becuase the first equation of mine  and you are same i did't mention that your solution is so different from mine .

@janhardo it is a good job but we don't have equation (50) from equation (47) you should achieve equation (50) and also equation (48) and (49), so what we must do in equation (47) to get them? i think @mmcdara know what we must do in here is a type of the equation he know about them and how achive them untill now he  did a great job for other question of mine i hope he do another answer for this case too .

@mmcdara  always you do something different i should read and practice on your code really i say that it is emazing i liked so much is so different from mine is like sword againest gun, but why you go to end and not finish the work i wish i can do like you and i wish always finish the work.
also i want another favior from you  i posted a new shap question like you did befor  but it is deffer and someone answer but is not like the paper and is not like your solution like you did, can you check my last question  and say your openion it is true or not ?

@nm it is so good let me give you advice if accepted from me it will be good can you watch my older post about this kind of solution which one of expert at maple answer to the problem and finded so good i am sure if you watch you will get more notion about it please watch , if you want update information please don't add at first comment add another new one  thank you so much i am wait for the new response

@nm  really i am glad to see this, it is emazing code this is show that are you  a expert at maple thank you so much, but the solution is not the same as in paper but it is so near to it i did a lot other stuff on it to get the exact as paper but can't reach out maybe i am wrong and i am sorry about that i think they are differ ?.

@mmcdara  i explaned in mp file, but maybe you didnt see it or didn't open it in begin
i did all stuff at there but i am not talented to replaced (G'/G)^2  in equation , don't be mad at me i am told you send me email for more information . again i am sorry i am work on this it is a while but is two week i am stuck at this step

@mmcdara first answer of your question is: for case sigma<0 it is mention in below of picture also i will upload other in here.
secondly, i don't know how you did really is emazing code and about equation you did a good job,

but mistak is in begin of equation  when you replace (s_ode_1 := eval(s_ode, S)) this is mistak you should take derivative S then replace G'' so you get w' and then again take derivative from S' again replace G'' then put do eval (S,S',S'') which is w,w',w'' put in equation then do other stuff i explain in mp file better please check also i will upload Image of other case of getting system equation in the paper also if you send me email i will send you whole paper which i can't upload paper here for you to see
check.mw

sigma>0

sigma=0 is

@janhardo i don't have problem in algebra i have problem with code if are you expert go a head we wait for your solution prove yourself  i did a trail i failed so go ahead yo do .

@mmcdara  i am sorry for spending your time and i am very glade to achieve this information , i want  solve whole problem by achieve system of equation and factoring them but i prefer to use other formula like in image if posible can you check how i can get thus system i did a lot trail and i will put my maple file here , explanation is like this replace eq(6) in eq(5) and use eq(7) when we get G'' replace eq(7) in eq(6) each time when you get derivative replace eq(7) then put all derivative in our ode equation then factoring all term in below of image write then we have a system of algebra equation then substitute must be satisfy .

aproach_of_GGGG.mw

@mmcdara  it will be totlay correct  if instead of sigma we write sigma=A[1]^2-A[2]^2 will be true but don't know where sigma come maybe it is integral constant of solution after simplify and factoring.
also we have three type for lambda >0 and lambda=0 if you do them too it will be a big help for me becuase it is your talent i can't go jump in your code i try to change to lambda<0 but  i failed, also i want solve the whole paper of yesterday when you done and told me trick of getting (G'/G)^2 =....., if you help me at there it will be a big help becuase i stuck at factoring and isolating (1/G)^i and (1/G)^i*diff(G(xi),xi)/G also instead each (G'/G)^2 we must do substitute for each case seperatly all the same if we do one case other will be easy,i hope help me at there really i am stcuk at there,  also i am intresting in your coding is like you know what you doing to be a perfect, your help is emazing for my job.

this is other case at same paper