110 citations · 158 across the 4 of their papers we have counts for
5 papers
The semiclassical modified nonlinear Schrödinger equation II: asymptotic analysis of the Cauchy problem. The elliptic region for transsonic initial data
Jeffery C. DiFranco, Peter D. Miller
We begin a study of a multi-parameter family of Cauchy initial-value problems for the modified nonlinear Schrödinger equation, analyzing the solution in the semiclassical limit. We…
On the modified nonlinear Schrödinger equation in the semiclassical limit: supersonic, subsonic, and transsonic behavior
Jeffery C. DiFranco, Peter D. Miller, Benson K. Muite
The purpose of this paper is to present a comparison between the modified nonlinear Schrödinger (MNLS) equation and the focusing and defocusing variants of the (unmodified) nonline…
Total integrals of global solutions to Painleve II
Jinho Baik, Robert Buckingham, Jeffery DiFranco +1
We evaluate the total integral from negative infinity to positive infinity of all global solutions to the Painleve II equation on the real line. The method is based on the interpla…
Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
Jinho Baik, Robert Buckingham, Jeffery DiFranco
The Tracy-Widom distribution functions involve integrals of a Painlevé II function starting from positive infinity. In this paper, we express the Tracy-Widom distribution functions…
The Semiclassical Modified Nonlinear Schroedinger Equation I: Modulation Theory and Spectral Analysis
Jeffery C. DiFranco, Peter D. Miller
We study an integrable modification of the focusing nonlinear Schroedinger equation from the point of view of semiclassical asymptotics. In particular, (i) we establish several imp…