Dynamical transitions between equilibria in a dissipative Klein-Gordon lattice
المؤلف | Frantzeskakis D.J. |
المؤلف | Karachalios N.I. |
المؤلف | Kevrekidis P.G. |
المؤلف | Koukouloyannis V. |
المؤلف | Vetas K. |
تاريخ الإتاحة | 2020-04-09T12:27:31Z |
تاريخ النشر | 2019 |
اسم المنشور | Journal of Mathematical Analysis and Applications |
المصدر | Scopus |
الرقم المعياري الدولي للكتاب | 0022247X |
الملخص | We consider the energy landscape of a dissipative Klein–Gordon lattice with a on-site potential. Our analysis is based on suitable energy arguments, combined with a discrete version of the Łojasiewicz inequality, in order to justify the convergence to a single, nontrivial equilibrium for all initial configurations of the lattice. Then, global bifurcation theory is explored, to illustrate that in the discrete regime all linear states lead to nonlinear generalizations of equilibrium states. Direct numerical simulations reveal the rich structure of the equilibrium set, consisting of non-trivial topological (kink-shaped) interpolations between the adjacent minima of the on-site potential, and the wealth of dynamical convergence possibilities. These dynamical evolution results also provide insight on the potential stability of the equilibrium branches, and glimpses of the emerging global bifurcation structure, elucidating the role of the interplay between discreteness, nonlinearity and dissipation. |
راعي المشروع | supported by NPRP grant # [ 9-329-1-067 ] from Qatar National Research Fund (a member of Qatar Foundation). The findings achieved herein are solely the responsibility of the authors. The authors D.J.F. and P.G.K. gratefully acknowledge the support of the Greek Diaspora Fellowship Program of Stavros Niarchos Foundation . |
اللغة | en |
الناشر | Academic Press Inc. |
الموضوع | Bifurcations of equlilibria Discrete Klein�Gordon equation Dissipation Limit set Nonlinear lattices Lojasiewicz inequality |
النوع | Article |
الصفحات | 546-576 |
رقم العدد | 1 |
رقم المجلد | 472 |
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