3 citations · 4 across the 8 of their papers we have counts for
9 papers
Long-time continuum limits for twisted Schrödinger lattices
Brian Choi
We prove polynomial-in-time Sobolev bounds on the approximation error between the twisted discrete nonlinear Schrödinger equation and its magnetic continuum limit. The analysis exp…
Speed of propagation of fractional dispersive waves
Brian Choi, Steven Walton
In this paper, we show that all non-trivial solutions of a broad class of nonlinear dispersive equations, whose linear evolution is governed by a dispersion relation under minimal…
Continuum Limit of 2D Fractional Nonlinear Schrödinger Equation
Brian Choi, Alejandro Aceves
We prove that the solutions to the discrete Nonlinear Schrödinger Equation (DNLSE) with non-local algebraically-decaying coupling converge strongly in to those…
Well-posedness of the mixed-Fractional Nonlinear Schrödinger Equation on
Brian Choi, Alejandro Aceves
We investigate the well-posedness theory of the 2-D fractional nonlinear Schrödinger equation (NLSE) with a mixed degree of derivatives. Motivated by models in optics and photonics…
Existence of Strong Solution for the Complexified Non-linear Poisson Boltzmann Equation
Brian Choi, Jie Xu, Trevor Norton +2
We prove the existence and uniqueness of the complexified Nonlinear Poisson-Boltzmann Equation (nPBE) in a bounded domain in . The nPBE is a model equation in nonline…
Multilinear Weighted Estimates and Quantum Zakharov System
Brian J Choi
We consider the compact case of one-dimensional quantum Zakharov system, as an initial-value problem with periodic boundary conditions. We apply the Bourgain norm method to show lo…
Modified Strichartz Estimate of the Periodic Fourth Order NLS
Brian J. Choi
We prove modified Strichartz estimates on the one-dimensional torus, that are adapted to a fourth-order dispersion relation, and use them to show global well-posedness of nonlinear…
Small Time Behavior and Summability for the Schrödinger Equation
Brian Choi
We consider the Carleson's problem regarding small time almost everywhere convergence to initial data for the Schrödinger equation, both linear and nonlinear on . It is…
Remark on the Adiabatic Limit of Quantum Zakharov System
Brian Choi
This paper is concerned with the low regularity well-posedness of the adiabatic limit of the quantum Zakharov system, which is a modified nonlinear Schrödinger equation (NLSE). As…