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Solitary waves in nonlinearly coupled oscillators in resonance. (English) Zbl 0768.76005

Summary: A simple model is used to describe the motion of a chain of anharmonically coupled harmonic oscillators whose frequencies are in \(s:1\) resonance, or in which combination resonances occur. It is shown that stable soliton-like excitations exist. Exact quantum states, approximate classical solutions, and numerical simulations of the classical equations are presented.

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
70K30 Nonlinear resonances for nonlinear problems in mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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