TY - JOUR
T1 - Generation of localization in a discrete chain with periodic boundary conditions
T2 - Numerical and analytical results
AU - Vakakis, Alexander F.
AU - Salenger, Gary
PY - 1998
Y1 - 1998
N2 - We study the generation of localization in a discrete chain composed of N subsystems and periodic boundary conditions. Strongly localized motions are studied; that is, time-periodic motions where nearly all of the energy is spatially confined to a single subsystem. For varying N, numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in-phase spatially extended solution. However, in the limit as N → ∞, the bifurcation point tends to infinity, and a smooth transition from localization to nonlocalization occurs. We then present an analytic technique to complement the numerical results. It is based on the matching local asymptotic expansions of a solution branch using Fade approximants. This leads to global analytic representations of the considered solutions, valid over the entire range of the control parameter.
AB - We study the generation of localization in a discrete chain composed of N subsystems and periodic boundary conditions. Strongly localized motions are studied; that is, time-periodic motions where nearly all of the energy is spatially confined to a single subsystem. For varying N, numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in-phase spatially extended solution. However, in the limit as N → ∞, the bifurcation point tends to infinity, and a smooth transition from localization to nonlocalization occurs. We then present an analytic technique to complement the numerical results. It is based on the matching local asymptotic expansions of a solution branch using Fade approximants. This leads to global analytic representations of the considered solutions, valid over the entire range of the control parameter.
KW - Fade approximations
KW - Nonlinear localization
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U2 - 10.1137/S0036139997316355
DO - 10.1137/S0036139997316355
M3 - Article
AN - SCOPUS:0032298027
SN - 0036-1399
VL - 58
SP - 1730
EP - 1747
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 6
ER -