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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2718

Title: Coupled Klein-Gordon equations and energy exchange in two-component systems
Authors: Khusnutdinova, Karima R.
Issue Date: 2007
Abstract: A system of coupled Klein-Gordon equations is proposed as a model for one-dimensional nonlinear wave processes in two-component media (e.g., long longitudinal waves in elastic bi-layers, where nonlinearity comes only from the bonding material). We discuss general properties of the model (Lie group classification, conservation laws, invariant solutions) and special solutions exhibiting an energy exchange between the two physical components of the system. To study the latter, we consider the dynamics of weakly nonlinear multi-phase wavetrains within the framework of two pairs of counter-propagating waves in a system of two coupled Sine-Gordon equations, and obtain a hierarchy of asymptotically exact coupled evolution equations describing the amplitudes of the waves. We then discuss modulational instability of these weakly nonlinear solutions and its effect on the energy exchange.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/2718
Appears in Collections:Pre-prints (Maths)

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