On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation (Q1958078)
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scientific article; zbMATH DE number 5792477
| Language | Label | Description | Also known as |
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| English | On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation |
scientific article; zbMATH DE number 5792477 |
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On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation (English)
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28 September 2010
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Summary: This paper is concerned with the instability of periodic travelling wave solutions of the modified Boussinesq equation. Periodic travelling wave solutions with a fixed fundamental period \(L\) are constructed by using Jacobi's elliptic functions. It is shown that these solutions, called dnoidal waves, are nonlinearly unstable in the energy space for a range of their speeds of propagation and periods.
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Boussinesq equation
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periodic travelling wave solutions
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instability
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