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Question: Find more solutions to a PDE

Question:Find more solutions to a PDE

yadaddy 96 Maple
pde differential-equations
August 21 2007
0
Hello! I have a quasilinear first-order PDE system and Maple gives me only the trivial zero-solution after some seconds of computations. I know from theory that there are nontrivial solutions to the PDE, too. Can I get them somehow (from for example Maple)? This is the 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(beta[2](u, v), v) = 1/4*I*exp(I*u)*alpha[2](u, v)+1/2*I*exp(I*(v+u))*beta[1](u, v)+1/2*I*(beta[2])(u, v), diff(alpha[2](u, v), v) = -I*exp(I*v)*beta[1](u, v), diff(beta[1](u, v), u) = -1/4*I*exp(-I*v)*alpha[2](u, v)-1/2*I*beta[1](u, v)-1/2*I*exp(-I*(v+u))*beta[2](u, v), diff(beta[1](u, v), v) = -1/4*I*exp(-I*u)*alpha[1](u, v)+1/2*I*beta[1](u, v)+1/2*I*exp(-I*(v+u))*beta[2](u, v), diff(beta[2](u, v), u) = -1/4*I*exp(I*v)*alpha[1](u, v)-1/2*I*exp(I*(v+u))*beta[1](u, v)-1/2*I*beta[2](u, v)} Thanks for help! Greetings, yadaddy.
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