Existence of Periodic Solutions in Inhomogeneous Toda Lattice

Abstract

A periodic Toda Lattice with impurity is investigated numerically. It isfound that there exist “resistant” periodic solutions for some specialvalues of the impurity mass. When perturbation and total energy becomesufficiently large, chaos is generated. However the resistant periodicsolutions do not disappear and two of them divide the chaos region into threesubregions which have different natures. Spatial coexistence of stationarychaos and nonstationary chaos is observed. Consequently, the existence ofsuch resistant periodic solutions suggests that solitonlike excitationspropagate without collapsing in media which include impurities.