KdV waves in atomic chains with nonlocal interactions

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.

revised version with corrected typos and minor improvements in the discussion of technical details; 20 pages, 4 figures

References in corpus (2)

• Counterpropagating Two-Soliton Solutions in the FPU Lattice
• Subsonic phase transition waves in bistable lattice models with small spinodal region

Cited by in corpus (6)

• Justification of the KP-II approximation in dynamics of two-dimensional FPU systems
• High-energy waves in superpolynomial FPU-type chains
• Solitary waves in atomic chains and peridynamical media
• Nonlinear Modulational Dynamics of Spectrally Stable Lugiato-Lefever Periodic Waves
• A uniqueness result for a simple superlinear eigenvalue problem
• Nonlinear and Nonlocal Eigenvalue Problems