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arXiv · 1405.3385

Justification of the log-KdV equation in granular chains: the case of precompression

Eric Dumas·Dmitry Pelinovsky
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Abstract

For travelling waves with nonzero boundary conditions, we justify the logarithmic Korteweg-de Vries equation as the leading approximation of the Fermi-Pasta-Ulam lattice with Hertzian nonlinear potential in the limit of small anharmonicity. We prove control of the approximation error for the travelling solutions satisfying differential advance-delay equations, as well as control of the approximation error for time-dependent solutions to the lattice equations on long but finite time intervals. We also show nonlinear stability of the travelling waves on long but finite time intervals.

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Eric Dumas, Dmitry Pelinovsky. 2014-05-14. Justification of the log-KdV equation in granular chains: the case of precompression. https://arxiv.org/abs/1405.3385

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