Dmitriev, S vKevrekidis, PG2024-04-262024-04-262006-01https://hdl.handle.net/20.500.14394/34110This is the pre-published version harvested from arXiv. The published version is located at http://iopscience.iop.org/0305-4470/39/23/003/We consider nonlinear Klein–Gordon wave equations and illustrate that standard discretizations thereof (involving nearest neighbours) may preserve either standardly defined linear momentum or standardly defined 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.Physical Sciences and Mathematicsarticle