delvin

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3 years, 7 days

MaplePrimes Activity


These are replies submitted by delvin

@nm 

Not to eliminate it altogether. I want to define the expression diff(H(xi), xi, xi)/H(xi)^2 as a new variable, so that all terms are rewritten in terms of this new variable, with no trace of the original function H(xi). The resulting equation will then be free of any derivatives and expressed entirely in terms of the new variable. I followed the instruction I learned from you before, but it didn't work. (algsubs)

I want to remove the derivatives in eq2 and the new function will not have any derivative terms at all. But the nature of the equation will be the same as equation 2.

@nm Thank you.

@janhardo 

No, you misunderstood my question. My question is about the code I sent. That image shows the results, but the code doesn't give the correct results. I wanted to know the errors in the code.

@nm 

Thank you very much.

@nm 

These are the steps that I wrote in order.

@Alfred_F 

Thanks

@Alfred_F 

No, there is no need for the equation you mentioned. With those substitutions in the image, the equation is completely solved.

@nm 

Thanks, but those parts are very important to me, for example, f is X and the derivative of f is Y and the rest.

@nm 

Hi,

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

 


 

 

 

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)

``

 

 

 

 

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

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

(2)

 

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)

 

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.

@nm 

I appreciate it.

@mmcdara

 thanks

Hi, 

Help 

@Carl Love 

Thank you for taking the time to do this.

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