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arXiv · 1503.02307

KdV waves in atomic chains with nonlocal interactions

Michael Herrmann·Alice Mikikits-Leitner
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Abstract

We consider atomic chains with nonlocal particle interactions and prove the existence of near-sonic solitary waves. Both our result and the general proof strategy are reminiscent of the seminal paper by Friesecke and Pego on the KdV limit of chains with nearest neighbor interactions but differ in the following two aspects: First, we allow for a wider class of atomic systems and must hence replace the distance profile by the velocity profile. Second, in the asymptotic analysis we avoid a detailed Fourier pole characterization of the nonlocal integral operators and employ the contraction mapping principle to solve the final fixed point problem.

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Michael Herrmann, Alice Mikikits-Leitner. 2015-03-08. KdV waves in atomic chains with nonlocal interactions. https://doi.org/10.3934/dcds.2016.36.2047

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