@janhardo  in figure , eq(12) contain x' which x' contain t,  is not about two lump is about two line next time i will come to two line first lets fix this y how construct the graph is so different from paper 

@janhardo we did some mistake and i am sure that mistak but i didn't have choice and i am going with it untill i figure out still i am stuck but is so better , i will upload here for you and i will asked a question about this situation if they don't delete, i want you work on it but don't answer that question untill new person which mean new idea come and help us 
first mistake of  our solution must contain t which i fixed , the only point is still i didn't figure out is this why our line is define like that (y=-beta*x/((a^2 + b^2)*alpha + 2*a*beta)-sqrt(30)/6 which is y=(-beta/((a^2 + b^2)*alpha + 2*a*beta)*x+sqrt(-3beta*a(a^2+b^2))/beta*b) i know half of this but this part i don't know where is related to(sqrt(-3beta*a(a^2+b^2))/beta*b)

-Y2-line.mw

@janhardo if need solution mentioned i will upload picture here

of old example which you used already

@janhardo  How plot two or three line in one graph like i mention in top together

@janhardo  it will  be great if add a plot with two y[1] and y[2] and lump of them are same how add  another plot for same picture?

@janhardo  is not three lump is a three line each one have a diffrent lump as velocity change 

@janhardo  i try to remove some extra from other example i got something new which is first time i saw this line is true but shape is not is that ok?
becuase in each paper which i saw when a line go from one lump to another lump they have same shape , but in here we don't have this pattern

can we check trajectory difference=0 like last time you did for this example 

i fixed this 

Download john.mw

Download john.mw

@janhardo this which you upload is for last example is not this example you plot function true a &b are true but this y is from old example , our is y=-x when a=b=1 is so clear from our mw file 

@janhardo this time is Run thanks so much, but john you didn't answer me in last comment , which is 
x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;
they number but why write like that? have any information? can be any number? 

also in paper mention the time variable t? but in here we don't have a t? and this is you done is a new thing by my openion if i am not wrong? 

john can you do for two and three lump? is same but instead of a & b you have a[1]&b[1] &a[2]&b[2] also for three lump if becuase i need to verify the work for this equation and other the picture already exist but i will upload here too, if you do that the work will be done 

@janhardo  why last part is not run, you did a great job, but some question is come up for me 

this equation (eq := y = -1/3*x - sqrt(30)/6;) must be -2/3*x why you subtract some thing  and also why you use (x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;) is a constant and when we replace (contourplot(U(x - x1, y - y1, a, b)) we shifted by this constant 

@janhardo  i need this plot one time you did but i don't know how , give me some more information when you plot 

@janhardo  i just don't know this trajectory this line and how construct them by my function by taking derivative and finding and don't know how use this (y=y+v_y*t) like you did watch the other example is more esier and  , in general i don't know about this y at all nothing explan in paper but i liked the graph i want the same graph for each equation when i solved but i don't know how in last part i am stuck , you did it but is so complicated , maybe you used i have to finded and used ,
if possible give me notion about this y and how plot  what is relation betwen of them?
in last code you take out difference the  trajectory and is zero which make it true what you finded ,is so good really 

@janhardo you did a great job really , but we need Dr.david for coding he is the the  best  for recoding this topic if he come in he will finish but if he undrestand topic , in the top code you have beta parameter but in here we have just a and b so is related to the old one you solved the wrong equation in the new question of mine you can see the different also in here in the question where is beta but you did something about trajectory i liked but i don't know how work with it 

@janhardo i watched more and is about trajectory explain more please if possible 

@janhardo  you seperate your code a lot i don't know why all of your code is part part , plot this can you? if possible give me some explanation too becuase i am not undrestand so good , explain in new post too maybe other can generate a good code you undrestand topic but other have better idea for recoding if they undrstand