Publication 24-CNA-007

Existence of solitary waves in particle lattices with power-law forces

Benjamin Ingimarson
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
bwi@andrew.cmu.edu

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rpego@cmu.edu

Abstract: We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ fixed-point arguments to find near-sonic solitary waves having scaled velocity profiles close to non-degenerate solitary-wave profiles of fractional KdV or generalized Benjamin-Ono equations. These equations were recently found to approximately govern unidirectional long-wave motions in these lattices.

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