Collins, Michael A. Solitary waves in nonlinearly coupled oscillators in resonance. (English) Zbl 0768.76005 Physica D 63, No. 1-2, 138-144 (1993). 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 Keywords:model of a polymer; quasi-one-dimensional molecular crystals; stable soliton-like excitations; quantum states; classical equations PDFBibTeX XMLCite \textit{M. A. Collins}, Physica D 63, No. 1--2, 138--144 (1993; Zbl 0768.76005) Full Text: DOI References: [1] Decius, J. C.; Hexter, R. M., Molecular Vibrations in Crystals (1977), McGraw-Hill: McGraw-Hill New York [2] Dolphin, D.; Wick, A., Tabulation of Infrared Spectral Data (1977), Wiley-Interscience: Wiley-Interscience New York [3] Mills, I. M., Theor. Chem., 1, 110 (1974) [4] Handy, N. C., Mol. Phys., 61, 207 (1987) [5] J. Chem. Phys., 81, 1115 (1984) [6] Sibert, E. L.; Hynes, J. T.; Reinhardt, W. P., J. Chem. Phys., 81, 1135 (1984) [7] Quack, M., Ann. Rev. Phys. Chem., 41, 839 (1990) [8] Clarke, D. L.; Collins, M. A., J. Chem. Phys., 92, 5602 (1990) [9] Clarke, D. L.; Collins, M. A., J. Chem. Phys., 93, 7894 (1990) [10] Clarke, D. L.; Collins, M. A., Biophysical J., 61, 316 (1992) [11] Kittel, C., Introduction to Solid State Physics (1966), Wiley: Wiley New York, Chap 5 [12] Toda, M., Prog. Theor. Phys. Suppl., 36, 113 (1966) [13] Collins, M. A., Chem. Phys. Lett., 77, 342 (1981) [14] Hochstrasser, D.; Mertens, F. G.; Buttner, H., Physica D, 35, 259 (1989) [15] Collins, M. A., Adv. Chem. Phys., 53, 225 (1983) [16] Rolfe, T. J.; Rice, S. A., Physica D, 1, 375 (1980) [17] Rosenau, P., Phys. Lett. A. Phys. Lett. A, Phys. Rev. B, 36, 5868 (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.