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Question: Assumption not working with PDE

Question:Assumption not working with PDE

yadaddy 96 Maple
August 27 2007
0
Hello! I have the following PDE: PDE := { diff(alpha[1](u, v), u) = -I*exp(I*u)*beta[1](u, v), diff(alpha[1](u, v), v) = -I*exp(-I*v)*beta[2](u, v), diff(alpha[2](u, v), u) = I*exp(-I*u)*beta[2](u, v), diff(alpha[2](u, v), v) = -I*exp(I*v)*beta[1](u, v), diff(beta[1](u, v), u) = (1/8*(I*exp(-I*v)*alpha[2](u, v)+(2*I)*beta[1](u, v)+(2*I)*exp(-I*(v+u))*beta[2](u, v)))*(a-1)-(1/8*(-I*exp(-I*u)*alpha[1](u, v)-(2*I)*beta[1](u, v)+(2*I)*exp(-I*(v+u))*beta[2](u, v)))*b, diff(beta[1](u, v), v) = (1/8*(I*exp(-I*u)*alpha[1](u, v)+(2*I)*beta[1](u, v)-(2*I)*exp(-I*(v+u))*beta[2](u, v)))*(a-1)-(1/8*(I*exp(-I*v)*alpha[2](u, v)+(2*I)*beta[1](u, v)+(2*I)*exp(-I*(v+u))*beta[2](u, v)))*b, diff(beta[2](u, v), u) = (1/8*(I*exp(I*v)*alpha[1](u, v)+(2*I)*exp(I*(v+u))*beta[1](u, v)-(2*I)*beta[2](u, v)))*(a-1)-(1/8*(I*exp(I*u)*alpha[2](u, v)+(2*I)*exp(I*(v+u))*beta[1](u, v)+(2*I)*beta[2](u, v)))*b, diff(beta[2](u, v), v) = (1/8*(-I*exp(I*u)*alpha[2](u, v)-(2*I)*exp(I*(v+u))*beta[1](u, v)-(2*I)*beta[2](u, v)))*(a-1)-(1/8*(I*exp(I*v)*alpha[1](u, v)+(2*I)*exp(I*(v+u))*beta[1](u, v)-(2*I)*beta[2](u, v)))*b}; fncs:={alpha[1](u,v),alpha[2](u,v),beta[1](u,v),beta[2](u,v)}; I have to assume a^2+b^2=1, a,b in IC (IC=comple numbers). So I write down: assume(a^2+b^2=1); and pdsolve(PDE,fncs) gives me the trivial solution, although having assumed a^2+b^2=1 and after DEtools[rifsimp](expand(PDE)); he mentions that he is assuming a^2+b^2 not to be 1, so he finds only the zero solution. If I solve with a,b in real numbers: a=sqrt(b^2-1) and solve the pde again, he explicitly finds a nontrivial solution, which is very ugly. But the problems here are, a,b are not necessary in IR and I think if Maple assumes a^2+b^2=1 with a,b in IC, the solution gets hopefully nicer. I also tried pdsolve(PDE,fncs) assuming(a^2+b^2=1); but this didn't help either. Can I change maybe the "Case" in the rifsimp to be the opposite of Maple using? Thank you for help! Greetings, yadaddy.
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