21 citations · 75 across the 14 of their papers we have counts for
15 papers
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…
Shallow water models for stratified equatorial flows
Anna Geyer, Ronald Quirchmayr
Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for…
Linear instability and uniqueness of the peaked periodic wave in the reduced Ostrovsky equation
Anna Geyer, Dmitry E. Pelinovsky
Stability of the peaked periodic waves in the reduced Ostrovsky equation has remained an open problem for a long time. In order to solve this problem we obtain sharp bounds on the…
Symmetric solutions of evolutionary partial differential equations
Gabriele Bruell, Mats Ehrnstrom, Anna Geyer +1
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and…
Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
Anna Geyer, Dmitry E. Pelinovsky
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we gi…
On the number of limit cycles for perturbed pendulum equations
Armengol Gasull, Anna Geyer, Francesc Mañosas
We consider perturbed pendulum-like equations on the cylinder of the form where are trigonometric…
Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude
Anna Geyer
Following a general principle introduced by Ehrnström et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all sym…
Singular solutions for a class of traveling wave equations arising in hydrodynamics
Anna Geyer, Víctor Mañosa
We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form , where is an a…
Non-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitude
N. Duruk Mutlubas, A. Geyer, B. V. Matioc
We prove that the flow map associated to a model equation for surface waves of moderate amplitude in shallow water is not uniformly continuous in the Sobolev space with $s>3/…
Traveling surface waves of moderate amplitude in shallow water
Armengol Gasull, Anna Geyer
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressibl…