---
OA_place: repository
OA_type: green
_id: '22044'
abstract:
- lang: eng
text: We prove that the small-data scattering map uniquely determines the nonlinearity
for a wide class of gauge-invariant, intercritical nonlinear Schrödinger equations.
We use the Born approximation to reduce the analysis to a deconvolution problem
involving the distribution function for linear Schrödinger solutions. We then
solve this deconvolution problem using the Beurling–Lax Theorem.
article_number: '015021'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
full_name: Killip, Rowan
last_name: Killip
- first_name: Jason
full_name: Murphy, Jason
last_name: Murphy
- first_name: Monica
full_name: Visan, Monica
id: 056daca0-b8d1-11f0-964f-f91054abf8ca
last_name: Visan
citation:
ama: Killip R, Murphy J, Vişan M. Determination of Schrödinger nonlinearities from
the scattering map. Nonlinearity. 2025;38(1). doi:10.1088/1361-6544/ada1bf
apa: Killip, R., Murphy, J., & Vişan, M. (2025). Determination of Schrödinger
nonlinearities from the scattering map. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ada1bf
chicago: Killip, Rowan, Jason Murphy, and Monica Vişan. “Determination of Schrödinger
Nonlinearities from the Scattering Map.” Nonlinearity. IOP Publishing,
2025. https://doi.org/10.1088/1361-6544/ada1bf.
ieee: R. Killip, J. Murphy, and M. Vişan, “Determination of Schrödinger nonlinearities
from the scattering map,” Nonlinearity, vol. 38, no. 1. IOP Publishing,
2025.
ista: Killip R, Murphy J, Vişan M. 2025. Determination of Schrödinger nonlinearities
from the scattering map. Nonlinearity. 38(1), 015021.
mla: Killip, Rowan, et al. “Determination of Schrödinger Nonlinearities from the
Scattering Map.” Nonlinearity, vol. 38, no. 1, 015021, IOP Publishing,
2025, doi:10.1088/1361-6544/ada1bf.
short: R. Killip, J. Murphy, M. Vişan, Nonlinearity 38 (2025).
das_tickbox: '1'
date_created: 2026-06-19T07:47:06Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2026-06-25T07:46:14Z
day: '01'
doi: 10.1088/1361-6544/ada1bf
extern: '1'
external_id:
arxiv:
- '2402.03218'
intvolume: ' 38'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2402.03218
month: '01'
oa: 1
oa_version: Preprint
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Determination of Schrödinger nonlinearities from the scattering map
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22083'
abstract:
- lang: eng
text: We prove global well-posedness for the cubic nonlinear Schrödinger equation
with nonlinearity concentrated on a homogeneous Poisson process.
article_number: '095020'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Benjamin
full_name: Harrop-Griffiths, Benjamin
last_name: Harrop-Griffiths
- first_name: Rowan
full_name: Killip, Rowan
last_name: Killip
- first_name: Monica
full_name: Visan, Monica
id: 056daca0-b8d1-11f0-964f-f91054abf8ca
last_name: Visan
citation:
ama: Harrop-Griffiths B, Killip R, Vişan M. The nonlinear Schrödinger equation with
sprinkled nonlinearity. Nonlinearity. 2025;38(9). doi:10.1088/1361-6544/ae022e
apa: Harrop-Griffiths, B., Killip, R., & Vişan, M. (2025). The nonlinear Schrödinger
equation with sprinkled nonlinearity. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ae022e
chicago: Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “The Nonlinear
Schrödinger Equation with Sprinkled Nonlinearity.” Nonlinearity. IOP Publishing,
2025. https://doi.org/10.1088/1361-6544/ae022e.
ieee: B. Harrop-Griffiths, R. Killip, and M. Vişan, “The nonlinear Schrödinger equation
with sprinkled nonlinearity,” Nonlinearity, vol. 38, no. 9. IOP Publishing,
2025.
ista: Harrop-Griffiths B, Killip R, Vişan M. 2025. The nonlinear Schrödinger equation
with sprinkled nonlinearity. Nonlinearity. 38(9), 095020.
mla: Harrop-Griffiths, Benjamin, et al. “The Nonlinear Schrödinger Equation with
Sprinkled Nonlinearity.” Nonlinearity, vol. 38, no. 9, 095020, IOP Publishing,
2025, doi:10.1088/1361-6544/ae022e.
short: B. Harrop-Griffiths, R. Killip, M. Vişan, Nonlinearity 38 (2025).
das_tickbox: '1'
date_created: 2026-06-19T08:27:54Z
date_published: 2025-09-15T00:00:00Z
date_updated: 2026-07-01T07:17:44Z
day: '15'
doi: 10.1088/1361-6544/ae022e
extern: '1'
external_id:
arxiv:
- '2405.01246'
intvolume: ' 38'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2405.01246
month: '09'
oa: 1
oa_version: Preprint
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The nonlinear Schrödinger equation with sprinkled nonlinearity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22046'
abstract:
- lang: eng
text: We show that solutions to the Ablowitz–Ladik system converge to solutions
of the cubic nonlinear Schrödinger equation for merely L2 initial data. Furthermore,
we consider initial data for this lattice model that excites Fourier modes near
both critical points of the discrete dispersion relation and demonstrate convergence
to a decoupled system of nonlinear Schrödinger equations.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
full_name: Killip, Rowan
last_name: Killip
- first_name: Zhimeng
full_name: Ouyang, Zhimeng
last_name: Ouyang
- first_name: Monica
full_name: Visan, Monica
id: 056daca0-b8d1-11f0-964f-f91054abf8ca
last_name: Visan
- first_name: Lei
full_name: Wu, Lei
last_name: Wu
citation:
ama: Killip R, Ouyang Z, Vişan M, Wu L. Continuum limit for the Ablowitz–Ladik system.
Nonlinearity. 2023;36(7):3751-3775. doi:10.1088/1361-6544/acd978
apa: Killip, R., Ouyang, Z., Vişan, M., & Wu, L. (2023). Continuum limit for
the Ablowitz–Ladik system. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/acd978
chicago: Killip, Rowan, Zhimeng Ouyang, Monica Vişan, and Lei Wu. “Continuum Limit
for the Ablowitz–Ladik System.” Nonlinearity. IOP Publishing, 2023. https://doi.org/10.1088/1361-6544/acd978.
ieee: R. Killip, Z. Ouyang, M. Vişan, and L. Wu, “Continuum limit for the Ablowitz–Ladik
system,” Nonlinearity, vol. 36, no. 7. IOP Publishing, pp. 3751–3775, 2023.
ista: Killip R, Ouyang Z, Vişan M, Wu L. 2023. Continuum limit for the Ablowitz–Ladik
system. Nonlinearity. 36(7), 3751–3775.
mla: Killip, Rowan, et al. “Continuum Limit for the Ablowitz–Ladik System.” Nonlinearity,
vol. 36, no. 7, IOP Publishing, 2023, pp. 3751–75, doi:10.1088/1361-6544/acd978.
short: R. Killip, Z. Ouyang, M. Vişan, L. Wu, Nonlinearity 36 (2023) 3751–3775.
das_tickbox: '1'
date_created: 2026-06-19T07:49:24Z
date_published: 2023-06-09T00:00:00Z
date_updated: 2026-06-25T07:54:44Z
day: '09'
doi: 10.1088/1361-6544/acd978
extern: '1'
external_id:
arxiv:
- '2206.02720'
intvolume: ' 36'
issue: '7'
keyword:
- Ablowitz–Ladik
- continuum limit
- cubic NLS
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2206.02720
mathsc:
- 35Q55
- 37K05
- 37K10
month: '06'
oa: 1
oa_version: Preprint
page: 3751-3775
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Continuum limit for the Ablowitz–Ladik system
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2023'
...
---
_id: '11701'
abstract:
- lang: eng
text: In this paper we develop a new approach to nonlinear stochastic partial differential
equations with Gaussian noise. Our aim is to provide an abstract framework which
is applicable to a large class of SPDEs and includes many important cases of nonlinear
parabolic problems which are of quasi- or semilinear type. This first part is
on local existence and well-posedness. A second part in preparation is on blow-up
criteria and regularization. Our theory is formulated in an Lp-setting, and because
of this we can deal with nonlinearities in a very efficient way. Applications
to several concrete problems and their quasilinear variants are given. This includes
Burgers' equation, the Allen–Cahn equation, the Cahn–Hilliard equation, reaction–diffusion
equations, and the porous media equation. The interplay of the nonlinearities
and the critical spaces of initial data leads to new results and insights for
these SPDEs. The proofs are based on recent developments in maximal regularity
theory for the linearized problem for deterministic and stochastic evolution equations.
In particular, our theory can be seen as a stochastic version of the theory of
critical spaces due to Prüss–Simonett–Wilke (2018). Sharp weighted time-regularity
allow us to deal with rough initial values and obtain instantaneous regularization
results. The abstract well-posedness results are obtained by a combination of
several sophisticated splitting and truncation arguments.
acknowledgement: The second author is supported by the VIDI subsidy 639.032.427 of
the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in
critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity.
2022;35(8):4100-4210. doi:10.1088/1361-6544/abd613
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces Part I. Stochastic maximal regularity and local existence.
Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/abd613
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.”
Nonlinearity. IOP Publishing, 2022. https://doi.org/10.1088/1361-6544/abd613.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces Part I. Stochastic maximal regularity and local existence,”
Nonlinearity, vol. 35, no. 8. IOP Publishing, pp. 4100–4210, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces Part I. Stochastic maximal regularity and local existence.
Nonlinearity. 35(8), 4100–4210.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.”
Nonlinearity, vol. 35, no. 8, IOP Publishing, 2022, pp. 4100–210, doi:10.1088/1361-6544/abd613.
short: A. Agresti, M. Veraar, Nonlinearity 35 (2022) 4100–4210.
date_created: 2022-07-31T22:01:47Z
date_published: 2022-08-04T00:00:00Z
date_updated: 2023-08-03T12:25:08Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/abd613
external_id:
arxiv:
- '2001.00512'
isi:
- '000826695900001'
file:
- access_level: open_access
checksum: 997a4bff2dfbee3321d081328c2f1e1a
content_type: application/pdf
creator: dernst
date_created: 2022-08-01T10:39:36Z
date_updated: 2022-08-01T10:39:36Z
file_id: '11715'
file_name: 2022_Nonlinearity_Agresti.pdf
file_size: 2122096
relation: main_file
success: 1
file_date_updated: 2022-08-01T10:39:36Z
has_accepted_license: '1'
intvolume: ' 35'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 4100-4210
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear parabolic stochastic evolution equations in critical spaces Part
I. Stochastic maximal regularity and local existence
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 35
year: '2022'
...
---
_id: '7637'
abstract:
- lang: eng
text: The evolution of finitely many particles obeying Langevin dynamics is described
by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz
multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki
model based on second order Langevin dynamics by analysing a system of particles
interacting via a pairwise potential. Key tools of our analysis are the propagation
of chaos and Simon's compactness criterion. The model we obtain is a small-noise
stochastic perturbation of the undamped McKean–Vlasov equation. We also provide
a high-probability result for existence and uniqueness for our model.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
- first_name: Johannes
full_name: Zimmer, Johannes
last_name: Zimmer
citation:
ama: Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised
Dean-Kawasaki model. Nonlinearity. 2020;33(2):864-891. doi:10.1088/1361-6544/ab5174
apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2020). From weakly interacting
particles to a regularised Dean-Kawasaki model. Nonlinearity. IOP Publishing.
https://doi.org/10.1088/1361-6544/ab5174
chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting
Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity. IOP Publishing,
2020. https://doi.org/10.1088/1361-6544/ab5174.
ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles
to a regularised Dean-Kawasaki model,” Nonlinearity, vol. 33, no. 2. IOP
Publishing, pp. 864–891, 2020.
ista: Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles
to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.
mla: Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised
Dean-Kawasaki Model.” Nonlinearity, vol. 33, no. 2, IOP Publishing, 2020,
pp. 864–91, doi:10.1088/1361-6544/ab5174.
short: F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.
date_created: 2020-04-05T22:00:49Z
date_published: 2020-01-10T00:00:00Z
date_updated: 2026-04-02T14:26:08Z
day: '10'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab5174
external_id:
arxiv:
- '1811.06448'
isi:
- '000508175400001'
intvolume: ' 33'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.06448
month: '01'
oa: 1
oa_version: Preprint
page: 864-891
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: From weakly interacting particles to a regularised Dean-Kawasaki model
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 33
year: '2020'
...
---
_id: '8697'
abstract:
- lang: eng
text: In the computation of the material properties of random alloys, the method
of 'special quasirandom structures' attempts to approximate the properties of
the alloy on a finite volume with higher accuracy by replicating certain statistics
of the random atomic lattice in the finite volume as accurately as possible. In
the present work, we provide a rigorous justification for a variant of this method
in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach
is based on a recent analysis of a related variance reduction method in stochastic
homogenization of linear elliptic PDEs and the locality properties of the TFW
model. Concerning the latter, we extend an exponential locality result by Nazar
and Ortner to include point charges, a result that may be of independent interest.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
citation:
ama: Fischer JL, Kniely M. Variance reduction for effective energies of random lattices
in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772.
doi:10.1088/1361-6544/ab9728
apa: Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies
of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity.
IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728
chicago: Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective
Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity.
IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728.
ieee: J. L. Fischer and M. Kniely, “Variance reduction for effective energies of
random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity,
vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.
ista: Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random
lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.
mla: Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies
of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity,
vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728.
short: J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.
corr_author: '1'
date_created: 2020-10-25T23:01:16Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2026-04-02T14:31:34Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/ab9728
external_id:
arxiv:
- '1906.12245'
isi:
- '000576492700001'
file:
- access_level: open_access
checksum: ed90bc6eb5f32ee6157fef7f3aabc057
content_type: application/pdf
creator: cziletti
date_created: 2020-10-27T12:09:57Z
date_updated: 2020-10-27T12:09:57Z
file_id: '8710'
file_name: 2020_Nonlinearity_Fischer.pdf
file_size: 1223899
relation: main_file
success: 1
file_date_updated: 2020-10-27T12:09:57Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
issue: '11'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 5733-5772
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variance reduction for effective energies of random lattices in the Thomas-Fermi-von
Weizsäcker model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 33
year: '2020'
...