Deniz Bilman
  • About
  • News
  • Publications
  • Teaching
  • Publications
    • 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
  • Blog
    • New paper!
    • RogueWaveInfiniteNLS.jl software package for Julia
    • Special session at the AMS Joint Math Meeting 2025 in Seattle, WA
  • In preparation
    • General rogue waves of infinite order: double-scaling asymptotics
    • Solitons of fractional order: interpolating between coherent structures
    • Infinite-order solutions of the modified Korteweg-de Vries equation
    • 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
  • Teaching
    • 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
    • Contact

New paper!

Aug 7, 2024·
Deniz Bilman
Deniz Bilman
· 1 min read
Density plot of the modulus of a rogue wave of infinite order

We have just submitted our paper titled General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective computation. See the publication.

Last updated on Aug 7, 2024
Deniz Bilman
Authors
Deniz Bilman
Assistant Professor
RogueWaveInfiniteNLS.jl software package for Julia Jul 15, 2024 →

© 2024 Deniz Bilman.

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