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Coupled Klein-Gordon equations and energy exchange in two-component systems
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.
History
School
- Science
Department
- Mathematical Sciences
Pages
1591779 bytesPublication date
2007Notes
This is a pre-print.Language
- en