On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation. (English) Zbl 1198.35215
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.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B35 | Stability in context of PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35C07 | Traveling wave solutions |
| 35C05 | Solutions to PDEs in closed form |
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