Intrinsic localized modes as solitons of the discrete Hirota equation

It is shown that intrinsic localized modes in a nonlinear lattice with a hard quartic nonlinearity are governed by the discrete Hirota equation. The requirement for the solution to be real results in a very restricted class of admissible soliton solutions corresponding to the localized excitations. In particular, it is shown that a single-soliton solution exists only at definite values of the amplitude and velocity. Two-soliton and multisoliton localized-mode solutions are reperesented. A small parameter of the problem is discussed. {} 1996 The American Physical Society.