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In this paper, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effec...
We show decay estimates for the propagator of the discrete Schrödinger and KleinGordon equations in the form {{\| {U(t)f} \|}_{{l^\infty}}} \leq C (1+|t|)^{-d/3}{{\| {f} \|}_{{l^1}}} . This impl...
For the nonlinear KleinGordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are, there...
We consider nonlinear KleinGordon wave equations and illustrate that standard discretizations thereof (involving nearest neighbours) may preserve either standardly defined linear momentum or standard...
In this paper, a theorem, which determines the linear stability of multibreathers excited over adjacent coupled oscillators in KleinGordon chains, is proven. Specifically, it is shown that for soft n...
In this work, we revisit the question of stability of multibreather configurations, i.e., discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We presen...

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