@Ronan thanks a lot, i change the equatoion becuase that issue and now i am back by your code i fixed thanks a lot ...

@janhardo not work always put mw file 

@sand15 by this pretty code we know which function we can use so, how i can add more function like exponential and even polynomial function like t, t^2 and so one and how many trigonometric and hyperbolic functiona ll of them i want all of them , beside this yesterday i solved another function which contain i  think 5 different function like g(t),p(t) q(t) and so on i will put that function in here too how we can do some iteration work for them  between them for all that function, the code is so pretty if possible add more function for the code also for generate second code is hard is not easy but maybe possible is just idea 

t-sand-mccdara.mw

one author use thus function just how i can test other  all of function i want the design and shape all of them to see which one i can put inside the explore option, like that p(t)=t, q(t)=cos(t), chi(t)=sinh and so one some interaction betwen them what we have if be like that

@dharr you are right about this ode, but the strange thing is this when i used for making my  general ode be zero is worked, i am in shock  with this i don't know use the function or not becuase is not solution of the auxiliary ode but is solution for general ode. i don't know what to do, please give me advise about that?

and i make it short the steps and remove some steps in case not be so long.

problem-.mw

@janhardo is like that i finished that 

line-3-done.mw

@janhardo  but i think  this plot is belong to mathematica program i didn't search but i have to plot different i am keep looking and thinking for get new idea which not repeated

@janhardo  i have to change my design of graph , matlab not so suir for thus kind of plotting 

something like that

@sand15 do you think i can do that and i don't want,  my research is stuck becuase of this step but at end with your help i finish the work this time is work and i construct 3 line thank to you,  i can't see the error like you do, i did watch and did some pertubation but didn't work in my hand 

@janhardo  they must transform for complex number 

design of graph my means? how many design we can have it for plots of lump even in 3D like this function 

2*((t*(-alpha*conjugate(lambda[1] + lambda[2]*I)^3 + b*conjugate(lambda[1] + lambda[2]*I) + c*r[2] + a) + 2*beta*(y*conjugate(lambda[1] + lambda[2]*I) + z*r[2] + x))/(2*beta) + (t*(-alpha*(lambda[1] + lambda[2]*I)^3 + b*(lambda[1] + lambda[2]*I) + c*r[1] + a) + 2*beta*(y*(lambda[1] + lambda[2]*I) + z*r[1] + x))/(2*beta))/(((t*(-alpha*(lambda[1] + lambda[2]*I)^3 + b*(lambda[1] + lambda[2]*I) + c*r[1] + a) + 2*beta*(y*(lambda[1] + lambda[2]*I) + z*r[1] + x))*(t*(-alpha*conjugate(lambda[1] + lambda[2]*I)^3 + b*conjugate(lambda[1] + lambda[2]*I) + c*r[2] + a) + 2*beta*(y*conjugate(lambda[1] + lambda[2]*I) + z*r[2] + x)))/(4*beta^2) - 4/((lambda[1] + lambda[2]*I - conjugate(lambda[1] + lambda[2]*I))^2*alpha))

can you plot by Ai you have lets see how many shape you have ?

@sand15 it is good to have you in here mapleprime need you...
i see yourse plot in below i run but didn't work i try to copy your function in my file again give me another error is nonsense a lot what the different betwen yours and mine? is look same 

Line-1-Done.mw

@janhardo  this is a little bit complecated, but you plotting in last is so pretty how many graph and hsape of design you can make it?

@sand15 you coding is nice, and also outcome, your coding is like maccdara ? he is expert, is been a while he missing ,

i am try to use your code but this unapply i cant work with it is not do any substitute your did write but with missing , your function eqfcomplex =f(x,y,z,t) i have use this in 2*ln(f)_x/f, your function must not contain any l[1] and l[2] , then from finding x and y when take derivative by t we put that point in that equation by name (eqp)  x=xp-(this take derivate by t from x[0] )*twe find critical point then we obtain the line by this function y=m*(x-x[0])+y[0] where x[0] and y[0] we can get by the critical point when t=0

i got this error this time

Line-1-Done.mw

@dharr i try to solve without making z=0 but at end i have to do z=1,  i got this error this time,

Error, invalid operator parameter name 

after i finish the plot after removing this issue i will send you, then judge me 

Line-1-Done.mw

@dharr is not wrong becuase when i plot 3D i make it t and z be constant so in here i just make z be number, i just don't know how make that D remove and my function run at there

@dharr  in lump plots we have another kinnd of plotting which show that thus lump how move when time,in most paper do that ,i did too to some but in here i got this problem, any news about long wave limit?

i can't fixed how i do eval z=0, in fact is not zero but i will make it zero becuase in this case i can plot it otherwise i don't think i can find the line along with moving lump i did my try but i didn't figure out, how fixed?

 Line-1-Done.mw