  We show that the non-homogeneous charged layer distribution of the LaAlO 3
/SrT iO 3 heterostructure undergoing interface reconstruction is the density
wave ground state of the well known anharmonic lattice model described by the
{\lambda}{\phi} 4 continuum model. The two dimensional planar structure of the
charged surfaces with alternating polarity leads to an effective one
dimensional model, with fermions coupled to the planar distortions acting as
long wavelength optical phonons in one dimension. The Hamiltonian with the
desired anharmonicity for describing the non-homogeneous density wave type
distortion is the same one that describes the fermion number fractionalization
in polyacetylene. The general solution of this theory is the Jacobi elliptic
sine function sn(x;k), which in the limiting case of lattice distortion being
localized gives the kink/anti-kink solution.
