Deniz Bilman
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  • Talks
    • Seminar, University of Oregon, Eugene, OR
    • Seminar, University of California Santa Cruz, Santa Cruz, CA
    • Seminar, University of Wisconsin-Madison, Wisconsin, MI
    • Seminar, Institut de Recherche Mathématique de Rennes, Rennes, France
    • AMS Fall Sectional Meeting, Special Session 'Integrability and Randomness', Tulane University, New Orleans, GA
    • WaDIB: Wave Dynamics, Integrability, and Beyond, Santa Margherita di Pula, Sardinia, Italy
    • Universality, Nonlinearity, and Integrability: In Honor of Percy Deift's 80th Birthday, KIAS, Seoul, Korea
    • Conference on 'Dispersive Integrable Equations: Pathfinders in Infinite-Dimensional Hamiltonian Systems', CIRM, Luminy, France
    • Seminar, Virginia Tech, Blacksburg, VA
    • IMACS Nonlinear Wave Conference, Special Session 'Advances in Integrable Systems and Inverse Scattering', Athens, GA
    • AMS Spring Sectional Meeting, Special Session 'Analysis of Nonlinear Wave Models', University of Kansas, Lawrence, KS
    • AMS Spring Sectional Meeting, Special Session 'Recent Advances in the Analysis of Integrable Systems', University of Kansas, Lawrence, KS
    • Seminar, SUNY University at Buffalo, Buffalo, NY
    • Seminar, University Washington, Seattle, WA
    • Seminar, 'Emergent phenomena in Nonlinear Dispersive Waves' Programme of Isaac Newton Institute, Northumbria University, Newcastle Upon Tyne, UK
    • SIAM Nonlinear Waves and Coherent Structures Conference 2024, Special Session 'Recent Developments in Dispersive Partial Differential Equations', Baltimore, MD
    • AMS Spring Sectional Meeting, Special Session 'Nonlinear Hamiltonian PDEs', Washington, DC
    • Seminar, University of Kansas, Lawrence, KS
    • Colloquium, University of Indiana-Purdue University at Indianapolis, Indianapolis, IN
  • Publications
    • Infinite-order rogue waves that are small (but not small in $L^2$)
    • Efficient computation of soliton gas primitive potentials
    • General rogue waves of infinite order: exact properties, asymptotic behavior, and effective numerical computation
    • Extreme superposition: high-order fundamental rogue waves in the far-field regime
    • RogueWaveInfiniteNLS.jl
    • Computation of large-genus solutions of the Korteweg-de Vries equation
    • Broader universality of rogue waves of infinite order
    • Far-field asymptotics for multiple-pole solitons in the large-order limit
    • On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data
    • Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
    • Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
    • Benchmarking numerical methods for lattice equations with the Toda lattice
    • A robust inverse scattering transform for the focusing nonlinear Schrödinger equation
    • Discrete integrable systems, Darboux transformations, and Yang–Baxter maps
    • Numerical inverse scattering for the Toda lattice
    • On the evolution of scattering data under perturbations of the Toda lattice
  • Teaching
    • Numerical Linear Algebra
      • Lecture 1
      • Lecture 2
      • Lecture 3
      • Lecture 4
      • Lecture 4 (Applications)
      • Lecture 5
      • Lecture 6
      • Lecture 7
      • Lecture 8
      • Lecture 10
      • Lecture 11
      • Lecture 12
      • Lecture 13
      • Lectures 14-15
      • Lecture 16
      • Lecture 17
      • Lecture 20
      • Lecture 21
      • Lecture 22
      • Lecture 23
      • Lecture 24
      • Lecture 25
      • Lecture 26
      • Lecture 27
      • Lecture 28
    • Ordinary Differential Equations
      • Lecture 1
      • Lecture 2
      • Lecture 3
      • Lecture 4
      • Lecture 5
      • Lecture 6
      • Lecture 7
      • Lecture 8
      • Lecture 9
      • Lecture 10
      • Lecture 11
      • Lecture 12
      • Lecture 13
      • Lecture 14
      • Lecture 15
      • Lecture 16
      • Lecture 17
      • Lecture 18
      • Lecture 19
      • Lecture 20
      • Lecture 21
      • Appendix 1
      • Appendix 2
    • Partial Differential Equations
      • Lecture 1
      • Lecture 2
      • Lecture 3
      • Lecture 4
      • Lecture 5
      • Lecture 6
      • Lecture 7
      • Lecture 8
      • Lecture 9
      • Lecture 10
      • Lecture 11
      • Lecture 12
      • Lecture 13
      • Lecture 14
      • Lecture 15
      • Lecture 16
      • Lecture 17
      • Lecture 18
      • Lecture 19
      • Appendix 1
  • Papers in Preparation
    • Solitons of fractional order: interpolating between coherent structures
    • Infinite-order solutions for the AKNS hierarchy and their asymptotic behavior
    • Asymptotic behavior of large-order soliton solutions of the modified Korteweg-de Vries equation
    • Far-field symptotics of large-order breathers for the sine-Gordon equation
    • Long-time development of initial data with spectral pole singularities
    • Long-time asymptotics for the Korteweg-de Vries equation
  • Film/TV Work
  • Outreaches
    • Member of the Organizing Committee, UC Math Bowl Competition (since Fall 2019)
    • Curriculum Developer and Instructor, CHANCE Program, UIC (2014, 2015, 2016)
  • Talks and Outreach

Infinite-order solutions for the AKNS hierarchy and their asymptotic behavior

May 1, 2024·
Deniz Bilman
Deniz Bilman
,
Elliot Blacksmith
,
Peter D. Miller
,
Giorgio Young
· 0 min read
Last updated on May 1, 2024
Deniz Bilman
Authors
Deniz Bilman
Associate Professor
← Solitons of fractional order: interpolating between coherent structures Jun 15, 2024
Asymptotic behavior of large-order soliton solutions of the modified Korteweg-de Vries equation Mar 1, 2024 →

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