## A. Geyer

18 records found

1

## Authored

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 negative eigenvalues of an associated Hessian operator changes in the existence region of smooth periodic ...

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 solitary waves behave similarly to the KP-II theory. This conclusion follows from our two main result ...

We develop a Korteweg-De Vries (KdV) theory for weakly nonlinear waves in discontinuously stratified two-layer fluids with a generally prescribed rotational steady current. With the help of a classical asymptotic power series approach, these models are directly derived from th ...

We solve the open problem of spectral stability of smooth periodic waves in the Camassa–Holm equation. The key to obtaining this result is that the periodic waves of the Camassa–Holm equation can be characterized by an alternative Hamiltonian structure, different from the stan ...

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 periodic functions with zero mean and the same period. We discover that the spectrum of a linearize ...

We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodi ...

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 literature review of all the available studies on this equation. Furthermore, we establish a novel result ...

The stability of the peaked periodic wave 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 exponential growth of the L ...

## Contributed

## Shallow Water Waves

### Deriving model equations for shallow water waves in a continuously stratified fluid over variable bottom topography

The goal of this paper is to study how waves move over a fluid in with an underlying current. Oceans displace debris and heat. Ocean models can be used to predict the movement of debris and even predict the effect of the movements of oceans on the climate. Mode ...