22 citations · 49 across the 11 of their papers we have counts for
12 papers
Scattering for the dispersion managed nonlinear Schrödinger equation
Mi-Ran Choi, Kiyeon Lee, Young-Ran Lee
We consider the dispersion managed nonlinear Schrdinger equations with quintic and cubic nonlinearities in one and two dimensions, respectively. We prove the global well-posedness…
Global existence versus finite time blowup dichotomy for the dispersion managed NLS
Mi-Ran Choi, Younghun Hong, Young-Ran Lee
We consider the Gabitov-Turitsyn equation or the dispersion managed nonlinear Schrödinger equation of a power-type nonlinearity \[ i\partial_t u+ d_\text{av} \partial_x^2u+\int_0^1…
Continuum limit related to dispersion managed nonlinear Schrödinger equations
Mi-Ran Choi, Young-Ran Lee
We consider the dispersion managed nonlinear Schrödinger equation with power-law nonlinearity and its discrete version of equations with step size . We prove that the so…
On dispersion managed nonlinear Schrödinger equations with lumped amplification
Mi-Ran Choi, Younghoon Kang, Young-Ran Lee
We show the global well-posedness of the nonlinear Schrödinger equation with periodically varying coefficients and a small parameter , which is used in optical-fiber…
Well-posedness of dispersion managed nonlinear Schrödinger equations
Mi-Ran Choi, Dirk Hundertmark, Young-Ran Lee
We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary av…
Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities
Mi-Ran Choi, Dirk Hundertmark, Young-Ran Lee
We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero averag…
Thresholds for Existence of dispersion management solitons for general nonlinearities
Mi-Ran Choi, Dirk Hundertmark, Young-Ran Lee
We prove a threshold phenomenon for the existence of solitary solutions of the dispersion management equation for positive and zero average dispersion for a large class of nonlinea…
Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-periodic Potential in Dimension Two
Yulia Karpeshina, Young-Ran Lee, Roman Shterenberg +1
We prove the existence of ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity a…
Structure of the fundamental solution of a nonconvex conservation law
Yong-Jung Kim, Young-Ran Lee
The structure of a signed fundamental solution of a conservation law is studied without the convexity assumption. The types of shocks and rarefaction waves are classified together…
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…
Spectral properties of a limit-periodic Schrödinger operator in dimension two
Yulia Karpeshina, Young-Ran Lee
We study Schrödinger operator in dimension two, being a limit-periodic potential. We prove that the spectrum of contains a semiaxis and there is a family of…
On non-local variational problems with lack of compactness related to non-linear optics
Dirk Hundertmark, Young-Ran Lee
We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These so…