Abstract
Exact anharmonic-localized-mode solutions to the discrete nonlinear Klein-Gordon (NKG) equation defined in a d -dimensional version of the simple cubic lattice are obtained by using the lattice Green's function method. For \(d{\geqslant}3\) there exists a critical value of the lattice anharmonicity for the appearance of the localized modes. An exact expression for the dispersion relation of a moving localized mode constituting a frequency band is obtained in terms of its shape functions. A comparison is made on the properties of moving and stationary or non-moving localized modes of the NKG equation with those of the d -dimensional discrete nonlinear Schrodinger equation. For d =1 one-localized-mode solution reduces in the continuum limit to the conventional one-soliton solution of the NKG equation.
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