1. What do you mean by "defining the image in relation to a chosen base"?

2. How are the base and T related to the image?

3. You ask "what I'm doing wrong", but you haven't said what you are doing.

I am using Maple 2021.2 on Ubuntu 20.04 (actually Ubuntu MATE 20.04).  I believe that my Ubuntu is entirely up to date. I have no crashing problems.

I suspect that the problem lies in a part of the worksheet that you have not shown.  To help diagnose the problem, upload the entire worksheet, and by that I don't mean cut-and-paste; upload your worksheet as an attachment. Ask here if you don't know how to do that.

@acer Thanks for the details of the redraw option. I don't have 2022, and 2021 does not seem to have it.  I will wait until I get my hands on 2022.

@acer The redraw=false option is new to me.  Where is it documented?  Searched but couldn't find.

Show the progress that you have made toward answering these homework questions, and ask specifically where you need help.

@Carl Love I see.  Thanks for pointing this out.

@Carl Love My reply to the OP was in reaction to his statement that he is finding three local minima and wishes to pick the best among them.  That doesn't inspire me with confidence that he understands the basics of the problem, hence my suggestion.

Forget about Maple for now. Try finding the minima by hand.  You will find that illuminating.

I can't understand at all what you are asking, and apparently neither does anyone else.

It will help if you could give one or two examples, consisting of:what you wish to type into Maple, and the result that you wish Maple to produce.

For example, you may say:

I want to type sin(2*x) into Maple and I want Maple to produce 2*sin(x)*cos(x).

Why would you expect a symbolic solution for this system?  You have two things going against you: (A) it is nonlinear; (B) is has variable coefficients.

You should be able to calculate a solution numerically if you specify the coefficients eta(t), gama(t), etc., and initial conditions.

Expanding on Kitonum's suggestion:

restart;
macro(D=`&D;`, I=`&I;`);
I = (1/64)*(D^4-d^4)*Pi;

@WillG The system, as you have posed, has no solution in general. Read the paper that you are referring to carefully to see what other assumptions are being made.

@tomleslie 

The conditions that I have imposed are not entirely arbitrary.  The PDE under consideration is a linearized version of the well-studied Korteweg de Vries (KdV) equations (look up KdV in Wikipedia).  It models dispersive waves on the entire real line (x going from minus infinity to plus infinity).  The solutions of interest are dispersive waves that propagate along the x axis while the far regions of the x axis are in undisturbed states, that is, the limits of the solution at plus/minus infinity are zero. Note that the OP specifically refered to dispersive waves.

For numerical calculations we replace infinity with finite values and move the "undisturbed" conditions to interval's boundaries.  The solution thus obtained is good for smallish values of time. When the wave interaction with the (artificial) boundaries becomes significant, the solution ceases to be meaningful.  To get good solutions for larger values of time, we solve the PDE over a larger x interval.  In the code I presented, I left the coordinates of the end points, a and b, as parameters in order to facilitate numerical experiments.

@ijuptilk That goes beyond my areas of interest.  I will let someone else to handle it.