Phase-Space Analysis of Elastic Vector Solitons in Flexible Mechanical Metamaterials

2025/10/17 by M. H. Duong, Duong, M. H., M.J. Reynolds +2 · 1 voice
Materials Science · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlocal and gradient elasticity in micro/nano structures #math-ph #nlin.PS

paper · pdf · doi:10.48550/arxiv.2510.19837

Abstract

The purpose of this paper is to propose a revised continuum model from the discrete system introduced in [Deng et.al., PRL, 2017] . Using a Galilean transformation, we obtain an equation governing the soliton solutions in the phase plane - a second-order nonlinear ODE related to the Klein-Gordon equation with quadratic nonlinearity. These admit the well-known sech² solutions, which we employ as an ansätz following [Deng et.al., PRL, 2017]. The resulting analysis yields soliton amplitudes and velocities that agree closely with numerical simulations, achieving an improvement of exactly 1/9 relative to the benchmark reported by the Harvard group.

Citations

• Homogenization and continuum limit of mechanical metamaterials

Discussions

• M. H. Duong, M. J. Reynolds: Phase-Space Analysis of Elastic Vector Solitons in Flexible Mechanical Metamaterials https://arxiv.org/abs/2510.19837 https://arxiv.org/pdf/2510.19837 https://arxiv.org/ht [bsky, 0 points, 0 comments]

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