## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
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- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
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### Open Access Journals

CPAA

We provide analytic solutions of the nonlinear differential
equation system describing the particle paths below
small-amplitude periodic gravity waves travelling on a constant
vorticity current. We show that these paths are not closed
curves. Some solutions can be expressed in terms of Jacobi
elliptic functions, others in terms of hyperelliptic functions. We
obtain new kinds of particle paths. We make some remarks on the
stagnation points which could appear in the fluid due to the
vorticity.

DCDS

In this paper we make a detailed analysis of the short-wavelength instability method for barotropic incompressible fluids.
We apply this method to edge waves in stratified water.
These waves are unstable to short-wavelength perturbations if their steepness exceeds a specific threshold.

DCDS

We consider the two-dimensional equatorial water-wave problem with constant vorticity in the $f$-plane approximation.
Within the framework of small-amplitude waves, we derive the dispersion relations and we find the analytic solutions of the
nonlinear differential
equation system describing the particle paths below such waves. We show that the solutions obtained are not closed curves. Some remarks on the stagnation points are also provided.

DCDS

We describe the physical hypotheses underlying the
derivation of
an approximate model of water waves.
For unidirectional surface shallow water waves moving over
an irrotational flow as well as over a non-zero vorticity flow,
we derive the Camassa-Holm equation by an interplay of
variational methods and small-parameter
expansions.

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