Similarity reduction, generalized symmetries and integrability of Belov-Chaltikian and Blaszak-Marciniak lattice equations

The Lie point symmetries of Belov-Chaltikian (BC) and Blaszak-Marciniak (BM ) lattice equations is derived. Using the symmetries similarity reduction f or both BC and BM lattice equations is obtained and show that each of the r educed equation possesses Lax representation and satisfies the singularity confinement criteria (a discrete version of the Painleve property) indicati ng their integrability. Two particular solutions of both the reduced equati ons are given explicitly. A systematic investigation for nonclassical symme tries of BC and BM lattice equations is carried out. Further, a sequence of conserved densities and generalized symmetries of both BC and BM lattice e quation are derived explicitly. The existence of a sequence of such symmetr ies is a predictor for integrability. (C) 2001 American Institute of Physic s.