Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum

S. V. Dmitriev; P. G. Kevrekidis; N. Yoshikawa

doi:10.1088/0305-4470/39/23/003

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Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum

S. V. Dmitriev·P. G. Kevrekidis·N. Yoshikawa

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Abstract

We consider nonlinear Klein-Gordon wave equations and illustrate that standard discretizations thereof (involving nearest neighbors) may preserve either standardly defined linear momentum or total energy but not both. This has a variety of intriguing implications for the ``non-potential'' discretizations that preserve only the linear momentum, such as the self-accelerating or self-decelerating motion of coherent structures such as discrete kinks in these nonlinear lattices.

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S. V. Dmitriev, P. G. Kevrekidis, N. Yoshikawa. 2005-06-01. Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum. https://doi.org/10.1088/0305-4470%2F39%2F23%2F003

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