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delvin

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@nm Hi,How do we get from equation ...

delvin 50
August 08 2024
0 0

@nm 

Hi,

How do we get from equation 1 to equation 3 with Maple by converting equations 2?

 


 

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pde:=i*diff(varphi[n](x,t),x)+(1+mu*(abs(varphi[n](x,t)))^(2))*(varphi[n+1](x,t)*exp(ik)+varphi[n-1](x,t)*exp(-ik))-nu*(abs(varphi[n](x,t)))^(2)*varphi[n](x,t)=0

i*(diff(varphi[n](x, t), x))+(1+mu*abs(varphi[n](x, t))^2)*(varphi[n+1](x, t)*exp(ik)+varphi[n-1](x, t)*exp(-ik))-nu*abs(varphi[n](x, t))^2*varphi[n](x, t) = 0

 (1)

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varphi[n](x,t)=chi[n]*exp(-i*vartheta*tau)

varphi[n](x, t) = chi[n]*exp(-i*vartheta*tau)

 (2)

 

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subs(varphi[n](x,t)=chi[n]*exp(-i*vartheta*tau),pde);

i*(diff(chi[n]*exp(-i*vartheta*tau), x))+(1+mu*abs(chi[n]*exp(-i*vartheta*tau))^2)*(varphi[n+1](x, t)*exp(ik)+varphi[n-1](x, t)*exp(-ik))-nu*abs(chi[n]*exp(-i*vartheta*tau))^2*chi[n]*exp(-i*vartheta*tau) = 0

 (3)

 

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q:=simplify(%);

exp(-2*Re(i*vartheta*tau)+ik)*mu*varphi[n+1](x, t)*abs(chi[n])^2-nu*abs(chi[n])^2*exp(-2*Re(i*vartheta*tau)-i*vartheta*tau)*chi[n]+exp(-2*Re(i*vartheta*tau)-ik)*mu*varphi[n-1](x, t)*abs(chi[n])^2+varphi[n+1](x, t)*exp(ik)+varphi[n-1](x, t)*exp(-ik) = 0

 (4)

``


 

Download convert.mw

@Mariusz Iwaniuk  Much obliged....

delvin 50
August 02 2024
0 0

@Mariusz Iwaniuk 

Much obliged.

@nm  I appreciate it....

delvin 50
August 02 2024
0 0

@nm 

I appreciate it.

@mmcdara  thanks...

delvin 50
June 11 2024
0 0

@mmcdara

 thanks

Guide...

delvin 50
December 24 2023
0 0

Hi, 

Help 

@Carl Love  Thank you for taking t...

delvin 50
December 06 2023
0 0

@Carl Love 

Thank you for taking the time to do this.

@Carl Love  I change 𝛯(𝜑), but i...

delvin 50
December 05 2023
0 0

@Carl Love 

I change 𝛯(𝜑), but it gives an error, what is the reason?

solutions:

 

J03.mw

@Carl Love  I’M REALLY GRATE...

delvin 50
December 04 2023
0 0

@Carl Love 

I’M REALLY GRATEFUL.

@dharr  The program does not run a...

delvin 50
December 02 2023
0 0

@dharr 

The program does not run and the system hangs.

@dharr  Jaco02.mw...

delvin 50
December 01 2023
0 0

@dharr 

Jaco02.mw

@dharr  I wrote Jacobi correct...

delvin 50
December 01 2023
0 0

@dharr 

I wrote Jacobi correctly in the program.

what does it mean?

you can help me?

@Carl Love  Will it be fixed later...

delvin 50
December 01 2023
0 0

@Carl Love 

Will it be fixed later?

 

No, I just wanted to enter in the attached program instead of definition.

@Carl Love If you intended the tanh...

delvin 50
December 01 2023
0 0

@Carl Love 

If you intended the tanh question to be independent of the error, I can attempt to answer it.

Okey

Your pde2 is not explicitly an equation because it doesn't consist of two expressions separated by =

It is the same image above the program. I wrote wrong?

@dharr  I changed jacoby to Jacoby...

delvin 50
December 01 2023
0 0

@dharr 

I changed jacoby to Jacoby but it didn't work?

@Carl Love What is the Differential...

delvin 50
December 01 2023
0 0

@Carl Love 

it is the Partial differential equation that becomes an ordinary differential equation in the second step.

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