About Me

I am an assistant professor of mathematics at the University of Cincinnati. My research interests lie primarily in nonlinear waves and integrable systems.

Previously, I was a postdoc at the University of Michigan working with Peter D. Miller. My PhD thesis advisor was Irina Nenciu and my thesis was on Hamiltonian perturbations of the doubly-infinite Toda lattice.

My research is supported by funds from the National Science Foundation and Simons Foundation.

Interests
  • Nonlinear waves
  • Integrable systems
  • Riemann-Hilbert problems
  • Dispersive PDEs
Education

  • PhD in Mathematics

    University of Illinois at Chicago

  • BSci & MSci in Mathematics

    Bogazici University

Recent News

New paper!

We have just submitted our paper on general rogue waves of infinite order.

RogueWaveInfiniteNLS.jl software package for Julia

We have just made the initial release of a software package for Julia to compute general rogue wave of infinite order solutions of the focusing nonlinear Schrödinger equation.

In preparation
Deniz Bilman, Peter D. Miller (2024). General rogue waves of infinite order: double-scaling asymptotics.
Deniz Bilman, Peter D. Miller (2024). Solitons of fractional order: interpolating between coherent structures.
Deniz Bilman, Elliot Blacksmith, Peter D. Miller, Giorgio Young (2024). Infinite-order solutions of the modified Korteweg-de Vries equation.
Deniz Bilman, Kurt Schmidt (2024). Asymptotic behavior of large-order soliton solutions of the modified Korteweg-de Vries equation.
Deniz Bilman, Robert Buckingham, Rajinder Mavi (2024). Far-field symptotics of large-order breathers for the sine-Gordon equation.
Deniz Bilman, Robert Jenkins, Peter Perry, Catherine Sulem (2024). Long-time development of initial data with spectral pole singularities.
Deniz Bilman, Percy Deift, Thomas Kriecherbauer, Ken Mclaughlin, Irina Nenciu (2024). Long-time asymptotics for the Korteweg-de Vries equation.
Publications

Click on the title of a publication to see more information, the abstract, featured plots or supplementary data. The ArXiv preprints do not reflect the final version of the published article.

Deniz Bilman, Peter D. Miller (2024). General rogue waves of infinite order: exact properties, asymptotic behavior, and effective numerical computation. Preprint.
Code ArXiv
Deniz Bilman, Peter D. Miller (2024). Extreme superposition: high-order fundamental rogue waves in the far-field regime. Memoirs of the American Mathematical Society.
Cite DOI ArXiv
Deniz Bilman, Peter D. Miller (2024). RogueWaveInfiniteNLS.jl. Software package for Julia.
Cite Code DOI
Deniz Bilman, Patrik Nabelek, Thomas Trogdon (2023). Computation of large-genus solutions of the Korteweg-de Vries equation. Physica D.
Cite Code DOI ArXiv
Deniz Bilman, Peter D. Miller (2022). Broader universality of rogue waves of infinite order. Physica D.
Cite DOI ArXiv
Deniz Bilman, Robert Buckingham, Deng-Shan Wang (2021). Far-field asymptotics for multiple-pole solitons in the large-order limit. Journal of Differential Equations.
Cite DOI ArXiv
Deniz Bilman, Thomas Trogdon (2020). On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data. Nonlinearity.
Cite DOI ArXiv
Deniz Bilman, Liming Ling, Peter D. Miller (2020). Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy. Duke Mathematical Journal.
Cite Code DOI ArXiv
Deniz Bilman, Robert Buckingham (2019). Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation. Journal of Nonlinear Science.
Cite DOI ArXiv
Deniz Bilman, Thomas Trogdon (2018). Benchmarking numerical methods for lattice equations with the Toda lattice. Applied Numerical Mathematics.
Cite Code DOI ArXiv
Deniz Bilman, Peter D. Miller (2017). A robust inverse scattering transform for the focusing nonlinear Schrödinger equation. Communications on Pure and Applied Mathematics.
Cite Video DOI ArXiv
Deniz Bilman, Sotiris Konstantinou-Rizos (2017). Discrete integrable systems, Darboux transformations, and Yang–Baxter maps. CRM Series in Mathematical Physics.
Cite DOI ArXiv
Deniz Bilman, Thomas Trogdon (2017). Numerical inverse scattering for the Toda lattice. Communications in Mathematical Physics.
Cite Code DOI ArXiv
Deniz Bilman, Irina Nenciu (2016). On the evolution of scattering data under perturbations of the Toda lattice. Physica D.
Cite DOI ArXiv