Acoustic Breathers in Two-Dimensional Lattices

We calculate breather solutions for a two-dimensional lattice with one acoustic phonon branch. We start from the case of a system with homogeneous interaction potentials. We then continue the zero-strain breather solution into the model sector with additional quadratic and cubic potential terms with the help of a generalized Newton method. The breather continues to exist but is dressed with a strain field. In contrast to the ac breather components, which decay exponentially in space, the strain field (which has dipole symmetry) should decay like $1/r^a$, $a=2\mathrm{}$. On our rather small lattice ( $70\times 70$) we find an exponent $a\approx 1.85$.