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Symmetry and monotonicity properties of solitary water-waves of positive elevation with supercritical values of parameter are established for an arbitrary vorticity. The proof uses the detailed knowledge of asymptotic decay of supercritical solitary waves at infinity and the method of moving planes.

- Vera Mikyoung Hur
- SIAM J. Math. Analysis
- 2006

The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitarywaves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a… (More)

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the… (More)

We study the dispersive character for waves on the one-dimensional free surface of an infinitely deep perfect fluid under the influence of surface tension. The main result state that, on average in time, the solution of the water-wave problem gains locally 1/4 derivative of smoothness in the spatial variable, compared to the initial state. The regularizing… (More)

- Vera Mikyoung Hur, Mathew A. Johnson
- SIAM J. Math. Analysis
- 2015

We study the stability and instability of periodic traveling waves for Korteweg-de Vries type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations. We then discuss when the associated linearized… (More)

- Robin Ming Chen, Vera Mikyoung Hur, Yue Liu, Robin Ming Chen, VERA MIKYOUNG, Yue Liu
- 2007

The rotation-modified Kadomtsev-Petviashvili equation describes small-amplitude, long internal waves propagating in one primary direction in a rotating frame of reference. The main investigation is the the existence and properties of its solitary waves. The existence and non-existence results for the solitary waves are obtained, and their regularity and… (More)

We discuss certain a priori geometric properties of two-dimensional steady gravity water waves with vorticity. The main result states that for an arbitrary distribution of vorticity, any periodic wave of finite depth with a single trough (a minimum over one period) is symmetric about a single crest (a maximum over one period) and the wave profile decreases… (More)

- MIKYOUNG HUR, Vera Mikyoung Hur
- 2008

We discuss certain a priori geometric properties of two-dimensional steady gravity water waves with vorticity. The main result states that for an arbitrary distribution of vorticity, any periodic wave of finite depth with a single trough (a minimum over one period) is symmetric about a single crest (a maximum over one period) and the wave profile decreases… (More)

- Vera Mikyoung Hur, Ashish Kumar Pandey
- Proceedings. Mathematical, physical, and…
- 2017

We determine the stability and instability of a sufficiently small and periodic travelling wave to long-wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of water waves and the Whitham equation to include nonlinearities of medium-amplitude waves. In the absence of the effects of… (More)