TY - JOUR

T1 - Non-local defect interaction in one-dimension

T2 - Weak versus strong non-locality

AU - Escaff, D.

N1 - © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

PY - 2011/3

Y1 - 2011/3

N2 - Defect interaction (kink-antikink interaction) is studied for a prototypical model for non-local interaction. Mathematically, it is a bistable integrodifferential model, where the non-local interaction is performed due to an integral kernel. The system is able to establish domains where it is in one of its two equilibria, separated by defects. It is shown that the defect interaction depends on the asymptotical behavior of the integral kernel. In the weak non-local regime, when the integral kernel decays faster than an exponential at infinitum, the defect interaction is exponentially weak. Hence, this case is qualitatively similar to the local one. On the other hand, in the strong non-local regime, when the integral kernel decays slower than an exponential at infinitum, the defect interaction is ruled by the asymptotical behavior of the integral kernel. In this case, the defect interaction is stronger, and could be characterized, for instance, by a power law. The effect of this transition (from the weak to strong non-locality) on the domain dynamics is discussed.

AB - Defect interaction (kink-antikink interaction) is studied for a prototypical model for non-local interaction. Mathematically, it is a bistable integrodifferential model, where the non-local interaction is performed due to an integral kernel. The system is able to establish domains where it is in one of its two equilibria, separated by defects. It is shown that the defect interaction depends on the asymptotical behavior of the integral kernel. In the weak non-local regime, when the integral kernel decays faster than an exponential at infinitum, the defect interaction is exponentially weak. Hence, this case is qualitatively similar to the local one. On the other hand, in the strong non-local regime, when the integral kernel decays slower than an exponential at infinitum, the defect interaction is ruled by the asymptotical behavior of the integral kernel. In this case, the defect interaction is stronger, and could be characterized, for instance, by a power law. The effect of this transition (from the weak to strong non-locality) on the domain dynamics is discussed.

UR - http://www.scopus.com/inward/record.url?scp=79958064387&partnerID=8YFLogxK

U2 - 10.1140/epjd/e2010-10323-8

DO - 10.1140/epjd/e2010-10323-8

M3 - Article

AN - SCOPUS:79958064387

VL - 62

SP - 33

EP - 38

JO - European Physical Journal D

JF - European Physical Journal D

SN - 1434-6060

IS - 1

ER -