7 citations · 10 across the 3 of their papers we have counts for
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On the transverse stability of smooth solitary waves in a two-dimensional Camassa-Holm equation
Anna Geyer, Yue Liu, Dmitry E. Pelinovsky
We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa--Holm equation. We show that transverse perturbations to one-dimensional sol…
Stability of smooth periodic traveling waves in the Degasperis-Procesi equation
Anna Geyer, Dmitry E. Pelinovsky
We derive a precise energy stability criterion for smooth periodic waves in the Degasperis--Procesi (DP) equation. Compared to the Camassa-Holm (CH) equation, the number of negativ…
Persistence of periodic traveling waves and Abelian integrals
Armengol Gasull, Anna Geyer, Víctor Mañosa
It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary…
Stability of smooth periodic traveling waves in the Camassa-Holm equation
Anna Geyer, Renan H. Martins, Fábio Natali +1
Smooth periodic travelling waves in the Camassa--Holm (CH) equation are revisited. We show that these periodic waves can be characterized in two different ways by using two differe…
Well-posedness of a highly nonlinear shallow water equation on the circle
Nilay Duruk Mutlubas, Anna Geyer, Ronald Quirchmayr
We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literatur…
Spectral instability of the peaked periodic wave in the reduced Ostrovsky equation
Anna Geyer, Dmitry E. Pelinovsky
We show that the peaked periodic traveling wave of the reduced Ostrovsky equations with quadratic and cubic nonlinearity is spectrally unstable in the space of square integrable pe…