  We construct new families of two-ended $O(m)\times O(n)$-invariant solutions
to the Allen- Cahn equation \Delta u+u-u3=0 in $\mathbb{R}^{N+1}$, with $N\ge
7$, whose zero level sets diverge logarithmically from the Lawson cone at
infinity. The construction is based on a careful study of the Jacobi-Toda
system on a given $O(m)\times O(n)$-invariant manifold, which is asymptotic to
the Lawson cone at infinity.
