Existence of solitary waves in particle lattices with power-law forces
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.09184
- arXiv:
- arXiv:2406.09184
- Bibcode:
- 2024arXiv240609184I
- Keywords:
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- Nonlinear Sciences - Pattern Formation and Solitons;
- Mathematics - Analysis of PDEs;
- Mathematics - Classical Analysis and ODEs;
- Primary 37K40;
- 70F45;
- Secondary 37K60;
- 70H09;
- 35R11
- E-Print:
- 30 pages