0 years, 79 days

## thank you @vv, when I run the foll...

thank you @vv,

when I run the following code:

restart:
local gamma:
PDE:=I*diff(u(x,t),t)+diff(u(x,t),x$2)+alpha*(abs(u(x,t))^2)*u(x,t)+ I*( gamma[1]*diff(u(x,t),x$3) + gamma[2]*(abs(u(x,t))^2)*u(x,t) + gamma[3]*diff((abs(u(x,t))^2),x)*u(x,t) )=0;

I get the following result:

what does abs(1,u(x,t))  mean?

or should I use the evalc as folows? Which one is correct defining the PDE?

PDE:=I*diff(u(x,t),t)+diff(u(x,t),x$2)+alpha*(evalc(abs(u(x,t))^2))*u(x,t)+ I*( gamma[1]*diff(u(x,t),x$3) + gamma[2]*(evalc(abs(u(x,t))^2))*u(x,t) + gamma[3]*diff((evalc(abs(u(x,t))^2)),x)*u(x,t) )=0;

## Thank you very much Dear @Kitonum. ...

Thank you very much Dear @Kitonum. The procedure is GREAT.

## Thank you very much dear @dharr, Y...

Thank you very much dear @dharr,

Yes, the Pde is complex. So, we can plot the absolute

I don't know what is the exact solution for the PDE. So, I don't guess initial or boundary conditions.

Is there no chance to find them? :)

## Fantastic...

It's great. Thank you very much @dharr,

Can we draw the 3D graphics of the solutions of the PDE for the appropriate parameters?

For example;

sigma:=1;
k:=-1;
c:=1;
varphi:=0;


## Thanks for such a good procedure @K...

Thanks for such a good procedure @Kitonum

1. I want the rectangle should be opaque and white. Because if there is no empty space within the plot, the rectangle will overlap the lines. I don't know whether the opaque rectangular is possible or not. If it is possible, we can overcome this situation as follows:

• In fact, I wanted to add an option to change the location of the legends like 'northeast' or 'southwest' etc. But I am not capable of achieving this.

2. Yes, you are right. If the procedure works for one function or 3 functions, etc, it will be nice. For doing this, can you help?

3. By defining G list, using the codes of Maple's plots package is a really good idea. I have not thought that or seen that before. Thanks also for this.

## Thank you dear @acer, I edited...

Thank you dear @acer, I edited the question.

I look forward to your valuable ideas for solving the question.

Best regards.

## Thanks, @Rouben Rostamian , yo...

Thanks, @Rouben Rostamian , you are right.

After you said, I exported the same graphic in Maple 2016, I got the better result than Maple 2020.

Do you think which version has better EPS exporting capability in Maple 2016-2019?

Is it 2018?

## Thanks for your interest Dear @Kito...

Thanks for your interest Dear @Kitonum,

If it is possible, could you share an example code?

## Thanks, dear @vv,Your figure can be...

Thanks, dear @vv,

Your figure can be acceptable but the texts of axis x and y and also texts of -10,-5,...5,10 are tiny. Yes, it can be increased by Maple.

But I will add the 3d graphics produced by Maple to the scientific articles. When I submitted the article which includes png figures like yours, the editor/reviewer wanted to correct the texts as vectorial texts.

What would you suggest to make those texts vectorial? to use another program?

## Dear @vv, I export the above figur...

Dear @vv,

I export the above figure to a high resolution .png. But the quality of figure is still very low.

Could you share your all Maple code in order to accomplish the example above?

## Thanks for your interest dear ...

Thanks for your interest dear @nm,

It's a nice idea. But, I don't understand the following step:

epspdf filename.ps
pdfcrop --margins 10  filename.pdf  filename.pdf

I think you run the code in latex. But I don't see the steps above in your Latex code?

\documentclass[11pt]{article}
\usepackage{graphicx}
\begin{document}
This is my graphics generated in Maple 2020.2

\includegraphics[width=0.9\textwidth]{file_name_here}
\end{document}

## Thanks @tomleslie,It is almost what...

Thanks, @tomleslie,

My goal was to find symbolically b[0],b[1], and U(x,t,y) and then was to test it for some numerical values of beta, alpha such as beta=2,alpha=2,... and then was to plot U(x,t,y) .

On the other hand, your code is almost what I want.

Just changing tanA:= to  tanA:=xi->

and changing

tanA*(sqrt(4*alpha*sigma - beta^2)/2*xi):

to

tanA(sqrt(4*alpha*sigma - beta^2)/2*xi):

I get the same results as Carl's love.

I want to ask one more question:

Suppose that b[0] has a minus and plus value such as b[0]:=±4+x+y, and suppose that we will calculate b[0]^3 and plot it (or more difficult calculations). My question is that what do you prefer in these cases? What is the trick for you?

## Thanks, @Carl Love.Your code is wha...

Thanks, @Carl Love.

Your code is what I want.

In fact,  even if I don' t change (x,y,t)-> test to unapply(test, [x,y,t]), I get same results as yours just changing your step 1 and 2.

1. In order to define functions, in which case do you prefer " ->" , in which case do you prefer "unapply" ?
2. On the other hand, suppose that b[0] has a minus and plus value such as b[0]:=±4+x+y, and suppose that we will calculate b[0]^3 and plot it (or more difficult calculations). My question is that what do you prefer in these cases? What is the trick for you?

## Many thanks, dear @Carl Love a...

Many thanks, dear @Carl Love and @Kitonum.

I understand much better now.

## Dear @Kitonum @Carl Love, What is ...

Dear @Kitonum @Carl Love,

What is the purpose of the left quote ` and also ~ operators?

What do you suggest to me for understanding the operators? (Examples, books, weblinks, etc.)

Thank you.

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