@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

@janhardo thanks john, it is something new , so i am looking for somehow  merge all part  together if this is a line How related to time variable t , when we have three lump in one graph with different time  How i can merge this with my code and give me my graph this is so importan ,it seems you know what you do and you know the idea behind this which i don't know it will be great if finish this work 

@dharr  i just looking for get new  idea but nothing come out  , i will updload some of this paper in case you see something new  but in all  of them don't saying anything about this , also john did something strange which make me confuse more  he find slop which you founded last time by dy/dx and used in slop equation  and make U(x,y,a,b) and instead of y i think he used function y=y0+m*(x-xo) instead of each a and b constant and ploted, x0 and y0 are intial, which i think is all of this are too close for reach but i can't know how , but i know is related to this equation  y=y0+m*(x-xo) all of them have this shape john combined them but he can't reach out too in each side something messing i needed this part for solve my puzzle 

the next paper is  which i did this too but can't reach line y again https://www.mapleprimes.com/questions/239905-How-Find-Line-For-Plotting-

lump-graph-john.mw

@janhardo  can you plot three lump last time you did also the color of each lump be different like picture 

@mmcdara  sorry i didn't know

@dharr incrideble, i will try find for other equations i hope no problem come up, dear Dr.David How about plot of this line along with lump , john did a plot for last problem but i can't read the code is a little bit  strange but the result is so clear  i upload him code here in case to get the idea of plotting and recoding , 
and i have a question, How define this 
Eqs 16,17
eqp := {x = xp - 5*(a^2 + b^2)*t, y = 10*a*t + yp};
after substitution must take it from this equation 
eqfcomplex := collect(evalc(eval(eval(eqf, p[2] = conjugate(p[1])), p[1] = a + b*I)), t);
my openion about that i tested and i take something which i don't know is true or not?
if we take a derivative from eqfcomplex by x when y=0 and by y when x=0 , we have to substitute the outcome part in (eqfcomplex) and we get our equation  which is  eq (16), also eq(17) but how substitute?

Dr-D-Line-derivative_add.mw

 line-lump-graph-John.mw

@dharr & @mmcdara  thank for both of you i combine them and the rest i will work on it , if possible work on this i stuck bad at here https://www.mapleprimes.com/questions/239914-How-Find-Line-In-Pde-Which-Can-Cut-Each

Dr.D-macdara-pde.mw

@dharr  i think the nonlinear part is wrong c[1] u[x$3,y] is linear but in seperating setting like non linear ? How?

Dr.D-pde.mw

@mmcdara  Dr.David make this and it answer to almost all of them except some of this question when we substitute we get (R) but in here we have zero, i don't know how find this (R) must be another way , i though maybe pde is wrong but is strange 

@dharr 

https://doi.org/10.1007/s11071-020-05611-9 (copyright material removed by moderator)

@dharr Dear Dr, Dr.macdara   answered this i saved him answer and worked, but i am very match with your code, and detail, and tonight i will delete https://www.mapleprimes.com/questions/239905-How-Find-Line-For-Plotting-  becuase i didn't reach the solution, and they don't let me asked another question like this even different,  i have 2 or 3  another paper to show How they reach this in this topic just this part remain, which really i am count on you to reach the solution , which will be finish just one step remain i hope tonight this step ended , i keep working to solve more paper to reach out ,but i can't see problem.
and he answered like this maybe get new idea
stop-working_mmcdara.mw

@janhardo  we can't see that trick but i try to post a new question and more example in case someone have idea for finding, becuase dublicate maybe i delete this if don't have problem

@janhardo i have enough paper and i have to solved but in all of them i can't find this line i have to show more example today i will try finish my job and collect all information in one package with more than at least three or 4 example to how find this line and velocity.