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. On our rather small lattice (70 x 70) we find an exponent a approximate to 1.85.