17 citations · 21 across the 5 of their papers we have counts for
6 papers
Infinite-order rogue waves that are small (but not small in )
Deniz Bilman, Peter D. Miller
General rogue waves of infinite order constitute a family of solutions of the focusing nonlinear Schrödinger equation that have recently been identified in a variety of asymptotic…
Suleimanov-Talanov self-focusing and the hierarchy of the focusing nonlinear Schrödinger equation
Robert J. Buckingham, Robert M. Jenkins, Peter D. Miller
We study the self-focusing of wave packets from the point of view of the semiclassical focusing nonlinear Schrödinger equation. A type of finite-time collapse/blowup of the solutio…
Rigorous Methods for Bohr-Sommerfeld Quantization Rules
Joanne Dong, Peter D. Miller, Giorgio Young
In this work, we prove Bohr-Sommerfeld quantization rules for the self-adjoint Zakharov-Shabat system and the Schrödinger equation in the presence of two simple turning points boun…
General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation
Deniz Bilman, Peter D. Miller
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schrödinger equation called general rogue waves of infinite order. These soluti…
The dbar steepest descent method for orthogonal polynomials on the real line with varying weights
K. T. -R. McLaughlin, P. D. Miller
We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form on the real line, as…
Metastability of Breather Modes of Time-Dependent Potentials
P. D. Miller, A. Soffer, M. I. Weinstein
We study the solutions of linear Schroedinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potenti…