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Question: what is problem why i can't get result?

Question:what is problem why i can't get result?

salim-barzani 950 Maple 2024
substitution pde differential-equations duplicate-question incomplete-question duplicate-account
March 05 2025
3
> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet); declare(u(x, y, z, t), quiet); declare(f(x, y, z, t), quiet)

``

 (1)
> 

thetai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)
> 

eqw := w[i] = (-1+sqrt(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1))/(2*mu)
> 

Bij := proc (i, j) options operator, arrow; -24*mu/(sqrt(1+(-4*beta*l[j]-4*delta*r[j]-4*alpha)*mu)*sqrt(1+(-4*beta*l[i]-4*delta*r[i]-4*alpha)*mu)-1+((2*r[i]+2*r[j])*delta+(2*l[i]+2*l[j])*beta+4*alpha)*mu) end proc
> 

NULL
> 

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))
> 

eqf := f(x, y, z, t) = theta1*theta2+Bij(1, 2)
> 

eqfcomplex := collect(evalc(eval(eval(eqf, l[2] = conjugate(l[1])), l[1] = a+I*b)), t)
> 

eq17 := u(x, y, z, t) = 2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2; equ := simplify(eval(eq17, eqfcomplex))

So we want to find a substitution that removes the time dependence from u. One way is to find the maximum and see how it moves. Here, the first solution gives what we want.

> 

ans := solve({diff(rhs(equ), x), diff(rhs(equ), y), diff(rhs(equ), z)}, {x, y, z}, explicit)
 

NULL

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