arashghgood

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These are replies submitted by arashghgood

@Preben Alsholm

dear Preben, consider eta as function of (x,t). then how can I solve it numerically? what are boundary and initial conditions?

as I know, without integral term the solution of the equation is sth like this (not exactly because the coeff are diferent)

eta(x,y,t) = A sech^2(k*x+l*y-v*t).

@Preben Alsholm 

I read that manual. Do you have an idea to solve such a equation numerically? (may be by built in functions or write a code)

thanks 

@tomleslie 

as you can see for K=1 the real and complex solutions exist. so K=1 is not interested. I look for (if it is possible) K=K1..K2 where all results (one or more) are imaginary for example. Or K=K3..K4 where all results (one or more) are complex, etc

@acer 

for example assume that Q and K are real. So Q:=alpha and K=k. and s:=7.44. I attached what I expect to see. I want to have plots like these.

 

@acer 

Dear acer

Thnaks for your reply. I think 2D plots are enough to study the relationships. in the cae of (i) (p-K plot) we can fix s.

In this post ( https://www.mapleprimes.com/questions/228566-Study-Complex-Equation-And-Plot-It ) I explain how I get this equation by hand. I am also interested in doing this process with maple. could you please take a look at this and help me?

@arashghgood 

Dear users

is there any idea to solve the issue

this equation can be rewrite like this

p/(1+sK^2)=-F(K,Q)/G(K,Q)

p/(1+sK^2)=-F(K,Q)/G(K,Q)

maybe it is helpful

@Christian Wolinski 

Thanks a lot for comments on the code.

One more question. Do you have an idea to plot eq and see the zeros of the eq, beyond what I did? and what should I do I I want to study just the real Or just the imaginary section of the K or Q. In  other words, in the case of pure imaginary K, what knid of changes should be done in the code. Is it enought to set the K=0..14*I ?

@Christian Wolinski 

Dear Christian Wolinski 844 , First of all, thank you for your code. It is very interesting for me.

Could you please explain me the last two lines?

map(`@`(evalf, subs), sols, map(`@`(abs, lhs - rhs), EQ));
  fnormal(%, Digits - 4);

@Christian Wolinski 

Note that we aim to solve the eq=0. the term cosh(Q) in the denominator doesn't have a role. I use the denominator to have a clear plot.

could you please explain your post in detail?

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