An effective description of the impact of inhomogeneities on the movement of the kink front in 2+1 dimensions

Abstract

In the present work we explore the interaction of a one-dimensional kink-like front of the sine-Gordon equation moving in 2-dimensional spatial domains. We develop an effective equation describing the kink motion, characterizing its center position dynamics as a function of the transverse variable. The relevant description is valid both in the Hamiltonian realm and in the non-conservative one bearing gain and loss. We subsequently examine a variety of different scenarios, without and with a spatially-dependent heterogeneity. The latter is considered both to be one-dimensional ($y$-independent) and genuinely two-dimensional. The spectral features and the dynamical interaction of the kink with the heterogeneity are considered and comparison with the effective quasi-one-dimensional description (characterizing the kink center as a function of the transverse variable) is also provided. Generally, good agreement is found between the analytical predictions and the computational findings in the different cases considered.

26 pages, 21 figures

References in corpus (2)

• Kink-antikink stripe interactions in the two-dimensional sine-Gordon equation
• Kink-inhomogeneity interaction in the sine-Gordon model

Cited by in corpus (2)

• Kink movement on a periodic background
• Collective coordinate descriptions of a kink in a driven-damped ${\varphi }^4$ model