solving two nonlinear multivariate equations

I will be so pleased if someone helps me solve these two equations to find approximate values of "p" and "q"

p.^2 .*(1-q).*(2.*q.*(1-p.^2)).^(2.*p) -2.*(1-p).*(1-q.*(1-p)).*(p+q.*(1-p))=0

((p+2.*q-2.*p.*q).*log2((p+(1-p).*q).*(1-q.*(1-p)))+(1-2.*q).*(1-p).*log2((1-q).*(1-p).*(q.*(1-p.^2)).^(1+p))-log2((1-q+p.*q)^2)+((1-p.^2).^2)+(1-q).*(-1+p))=0

Note: There is a constraint that both variables must be limited to interval of [0,1]

Thanks in advance!

Answer 1

[Matt J]

Sorry, my previous answer was wrong. There are no solutions to your equations. In a previous post, it was shown to you that the first equation can be satisfied only by p=0 or p=1. Further, when p=0, only q=0 or q=1 are solutions.

When p=1, the expression

 log2((1-q).*(1-p).*(q.*(1-p.^2)).^(1+p))

in the second equation is undefined, so p=1 is eliminated as a possibility.

When p=0, the expression

 log2((p+(1-p).*q).*(1-q.*(1-p)))

in the second equation is undefined whenever q=0 or q=1, which are the only possibilities that satisfy the first equation.

So, no solutions.... :-(