28 citations · 34 across the 7 of their papers we have counts for
7 papers
Smoothing estimates for weakly nonlinear internal waves in a rotating ocean
M. B. Erdogan, N. Tzirakis
In this paper we study the effect of rotation on nonlinear wave phenomena in weakly dispersive media modeled by the Korteweg-de Vries equation on the real line. It is well known th…
Regularity properties of the Zakharov system on the half line
Burak Erdogan, Nikolaos Tzirakis
In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellpos…
Fractal solutions of linear and nonlinear dispersive partial differential equations
V. Chousionis, M. Burak Erdoğan, Nikolaos Tzirakis
In this paper we study fractal solutions of linear and nonlinear dispersive PDE on the torus. In the first part we answer some open questions on the fractal solutions of linear Sch…
High frequency perturbation of cnoidal waves in KdV
M. B. Erdoğan, N. Tzirakis, V. Zharnitsky
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of fi…
Exponential decay of dispersion managed solitons for vanishing average dispersion
M. Burak Erdogan, Dirk Hundertmark, Young-Ran Lee
We show that any solution of the Gabitov-Turitsyn equation describing dispersion managed solitons decay exponentially in space and frequency domains. This confirms in the aff…
Near-linear Dynamics for Shallow Water Waves
M. B. Erdogan, N. Tzirakis, V. Zharnitsky
It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequ…
Dispersive estimates for Schroedinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II
Mehmet Burak Erdogan, Wilhelm Schlag
We consider non-selfadjoint operators of the kind arising in linearized NLS and prove dispersive bounds for the time-evolution without assuming that the edges of the essential spec…