22 citations · 49 across the 11 of their papers we have counts for
8 papers · 1 filter
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…
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…