Localized modes in a two-degree-coupling periodic system with a nonlinear disordered subsystem

Abstract

The localized modes in a two-degree-coupling periodic system with infinite number of subsystems and having one nonlinear disorder are analyzed by using the Lindstedt–Poincare (LP) method. The governing equation with the standard form in which the linear terms are uncoupled for subsystems, is derived by using the U-transformation technique. Three types of localized modes, i.e., symmetric, anti-symmetric and asymmetric modes, are found by the LP method. It is shown that the nondimensional parameter η ( i.e., (16k c /3γ 0)A max −2) controls the type, number, stability and localized level of the modes.