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Solitary wavepackets from oscillatory non-linear equations with damping

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Abstract

In this paper, an infinite family of solutions describing solitary wave packets with a finite number of nodes is presented. These structures arise from the study of damping in the framework of non-linear ordinary differential equations with oscillatory behaviour. Usually one expects to find effects of this kind in physical systems described by a set of partial differential equations. The standard argument is that the non-linear term acts against the dispersive flux and this balance explains the appearance of solitary waves. Here we show that the non-linear oscillatory behaviour can also balance the effect of damping in special cases. The theory used to discriminate among the various possibilities is plain Painlevé analysis. Several physical applications are briefly discussed.

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  1. Física Fundamental, Facultad de Ciencias, Universidad de Salamanca, 37008, Salamanca, Spain

    José M. Cerveró

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  1. José M. Cerveró
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Correspondence to José M. Cerveró.

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Cerveró, J.M. Solitary wavepackets from oscillatory non-linear equations with damping. Nonlinear Dyn 67, 63–69 (2012). https://doi.org/10.1007/s11071-011-9957-x

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