Articles and Manuscripts

More Publications

You can also access a list of my publications here. Please scroll below for details of each publication and click on the publication to read the abstract.

In preparation, 2018

[55 pages]
Submitted (under review), 2018

[84 pages]
Communications in Pure and Applied Mathematics, 2017

[27 pages]
To appear in Appl. Numer. Math., 2017

[65 pages]
CRM Series in Mathematical Physics, Springer, 2017

[74 pages]
Communications in Mathematical Physics, 2017


A Robust Inverse Scattering Transform for Arbitrary Spectral Singularities

Development of a robust inverse scattering transform to treat arbitrary spectral singularities, in particular including rogue wave solutions of nonlinear integrable dispersive PDEs.

Numerical Inverse Scattering Transforms

Making solutions of integrable nonlinear dispersive wave equations computationally available to the nonlinear waves community using their Riemann-Hilbert problem representations via developing numerical inverse scattering transform tools. Riemann-Hilbert problems play the role of Fourier-type integral representations we have for solutions of linear problems.

Solitary Wave Resolution: Long-Time Asymptotics for Near-Integrable Systems

Long-time asymptotics for perturbations of integrable wave models that admit solitary wave solutions.

Stability Properties of Rogue Waves and Asymptotics for Large-Order Coherent Structures

Analysis and prediction of rogue waves in context of a Cauchy initial value problem, asymptotic properties of large-order coherent structures such as ‘high-order-pole’ solitons appearing in nonlinear dispersive integrable PDEs.


Recent & Upcoming 10 talks

A Robust Inverse Scattering Transform and Very Large Rogue Waves
Apr 17, 2019 9:00 AM
What do Riemann-Hilbert problems tell us about nonlinear waves?
Apr 1, 2019 10:00 AM
A Robust Inverse Scattering Transform and Very Large Rogue Waves
Nov 8, 2018 2:00 PM
Extreme superposition: Rogue waves of infinite order and the Painlevé-III hierarchy
Jul 7, 2018 8:30 AM
A Robust Inverse Scattering Transform and Very Big Rogue Waves
Apr 3, 2018 11:00 AM
Riemann-Hilbert Problems: Asymptotics & Computation
Mar 1, 2018 4:00 PM
Riemann-Hilbert Problems: Asymptotics & Computation
Dec 1, 2017 3:00 PM
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
Sep 27, 2017 3:10 PM
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
Jul 15, 2017 4:30 PM

Recent Posts

To be held on October 20-21, 2018 in Ann Arbor, MI. Organizers: Deniz Bilman, Peter D. Miller, Amber Music, Guilherme Silva.



Courses & Lecture Notes

I am teaching Math 454: Boundary Value Problems for Partial Differential Equations in Spring 2019. This is a course devoted to the use of Fourier series and other orthogonal expansions in the solution of initial-value and boundary-value problems for second-order linear partial differential equations.

Course information

Lecture Notes and Course Material

Below is a list of topics/courses for which I have developed online lecture notes using Jupyter notebooks while I was teaching the courses.

Interactive Lecture Notes for Differential Equations (Math 216)

Interactive online (Jupyter) lecture notes from Math 216: Introduction to Differential Equations taught at the University of Michigan in Spring 2016, Fall 2017, and Spring 2018. You may also find some separate handwritten material from the series of examples titled Here’s How I’d Do It.

Interactive Lecture Notes for Numerical Analysis (Math 471)

Interactive online (Jupyter) lecture notes for Math 471: Introduction to Numerical Analysis taught at the University of Michigan in Winter 2019.


  • denizbilman
  • 1830 East Hall, University of Michigan, Ann Arbor, MI 48109, USA
  • T 12-2 PM and W 12-1 PM in 1830 East Hall