Generalized nonlinear Schrödinger equation for longitudinal deformation waves in an acoustic metamaterial

A. V. Porubov

Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We asymptotically obtain a generalized Schrödinger equation for nonlinear deformation waves in a metamaterial. It turns out to be analogous to the Sasa–Satsuma equation derived for optical waves. We study distinctions in the solution in the form of localized deformation waves related to the generalization of the Schrödinger equation.

Keywords: acoustic metamaterial, nonlinear wave, nonlinear modulation.

Received: 03.03.2025
Revised: 27.03.2025

DOI: 10.4213/tmf10965

 English version: Theoretical and Mathematical Physics, 2025, 224:3, 1664–1670

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