@acer i owe you and thank you so much this is help me and make me fly right now with this emazing code.

@acer i don't belive that how you did it that is exactly what i am looking for but one step remain   , when i enter the last program geve me the parameter but it will be so better if be like that instead of just  be a number in bracket

[0.1,0.2,0.3,...] if be like that will be better [alpha=0.1,beta=0.2,gamma=0.3,...] i want to to this too it will be more amazing

and it can be both together in one program or i must seperatly used them  for parameter and for function can i merge them in one program for parameter and function?

@acer ok never mind about parameter search (is like searching for a kind of graph like generating graph by parameter graph name kind of kink, w-shap, bell-shap, wave and so on ) i can look for parameter by your code exploring is a good code and it is work for me
when i manipulate parameter and get my graph i want inpute thus parameter in M(our function), becuase i must transfer this function with substituting all parameter in M
how i can do that?

@nm  can you upload here, manager delete it watch my above comment you will see he delete it , it is new and i have a lot question about that but becuase manager i  reduce my questions. and this program i uploaded belonge to him he did that.
and i know it is work if change alpha but i want after i sketch graph by manipulate paramater i want substitute thus parameters in my function M i need that outcome with substituting paramaeters
also if there is any other idea it will be so good for ploting

@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