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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 c...
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| Format: | Default Preprint |
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2007
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| Online Access: | https://hdl.handle.net/2134/2718 |
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| _version_ | 1818175104347013120 |
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| author | Karima Khusnutdinova |
| author_facet | Karima Khusnutdinova |
| author_sort | Karima Khusnutdinova (1247967) |
| collection | Figshare |
| description | 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. |
| format | Default Preprint |
| id | rr-article-9383567 |
| institution | Loughborough University |
| publishDate | 2007 |
| record_format | Figshare |
| spelling | rr-article-93835672007-01-01T00:00:00Z Coupled Klein-Gordon equations and energy exchange in two-component systems Karima Khusnutdinova (1247967) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified 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. 2007-01-01T00:00:00Z Text Preprint 2134/2718 https://figshare.com/articles/preprint/Coupled_Klein-Gordon_equations_and_energy_exchange_in_two-component_systems/9383567 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified Karima Khusnutdinova Coupled Klein-Gordon equations and energy exchange in two-component systems |
| title | Coupled Klein-Gordon equations and energy exchange in two-component systems |
| title_full | Coupled Klein-Gordon equations and energy exchange in two-component systems |
| title_fullStr | Coupled Klein-Gordon equations and energy exchange in two-component systems |
| title_full_unstemmed | Coupled Klein-Gordon equations and energy exchange in two-component systems |
| title_short | Coupled Klein-Gordon equations and energy exchange in two-component systems |
| title_sort | coupled klein-gordon equations and energy exchange in two-component systems |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/2718 |