| Abstract: |
| In this talk I will discuss the existence and (in)stability of periodic waves for equations of KdV-Burgers type with a source. In particular, I will discuss the existence of small-amplitude periodic waves for the KdV-Burgers-Fisher equation (with a source of Fisher-KPP type), which arise from a local bifurcation on the wave speed. Moreover, these periodic waves are spectrally unstable as solutions to the PDE, that is, the Floquet (continuous) spectrum of the linearization around each periodic wave intersects the unstable half plane of complex values with positive real part. I will also discuss how to conclude the orbital (nonlinear) instability of the waves departing from the
spectral instability result for a general family of equations. This is joint work with Anna Naumkina and Raffaele Folino (IIMAS, UNAM). |
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