Integrable Partial Differential Equations: Geometry, Asymptotics, and Numerics.

Rezultaty

By this date at least a public lecture on subjects related with the project and aimed at the wider public will be delivered at each node.

Conference at Unimib

First general Conference of the Project. The main focus will be on WP2( (Near-to) Integrable PDEs and Applications), state of the art review and novel developments. The state of the art concerning WP3 and WP4 will be also reviewed. The conference will be organized by Unimib. The entire network will participate, and attendance by experts outside the consortium will also be encouraged.

Public Lecture 2

Within month 21 and month 70 at least a public lecture on subjects related with the project and aimed at the wider public will be delivered at each nodeThe lectures will be also occasion to present and show the video gallery.

Conference at SISSA

Third conference of the project. The main focus will be on WP3 (Isomonodromic deformations, Painlevé Equations and random objects), state of the art review and novel developments. The state of the art concerning WP2 and WP4 will also be reviewed. The conference will be organized by SISSA. The entire network will participate, and attendance by experts outside the consortium will also be encouraged.

Conference at UBFC

Second general Conference of the project. The main focus will be on WP4 (Numerical Approaches), state of the art review and novel developments. The state of the art in WP2 and WP3 will also reviewed.The conference will be organized by UBFC (in particular University of Bourgogne). The entire network will participate, and attendance by experts outside the consortium will also be encouraged.

Monograph

Publication of a monograph directed to graduate students to present the research activities of the network to a larger audience in a more accessible way than journal publications. In this monograph integrable systems techniques are compared to PDE methods for certain integrable equations. This will allow to asses pro’s and con’s of the two approaches to the same type of equations, providing an important compendium accessible to both communities. It will also help to identify strategies to apply integrable system techniques to non-integrable PDEs which is at the heart of the present project.

Release of Numerical code libraries

"Libraries of numerical programs will be developed. This will allow the participants of the project to use state-of-art numerical techniques to be developed by those participants actively working in WP4 (Numerical Methods). These novel numerical approaches will allow to address questions which are up to now out of reach of standard numerical techniques. During the first half of the project, the use of this numerical library will be restricted (also for testing reasons) to the members of the Consortium. By the end of the project, the libraries will be made freely available to the scientific community at large. An exception will be made for codes with potential commercial interest, that will be protected by software patents.The libraries are envisaged to comprise:1) Implementation of geometric and symplectic integrators for integrable and almost integrable PDEs.2) Development of ""boundary integral"" and multi-domain spectral methods for coupled Internal-Surface Wave systems.3) Painlevé equations.4) Numerical treatment of compact Riemann surfaces."

Web Page

Web page of the network, created and constantly updated with the description of the goals and the actions of the network, both scientific and organizational. The web page will also have a section devoted to the large public, for outreach purpose.

video gallery

Realization of an online video gallery with typical solutions of dispersive PDEs. Thisgallery will combine information in the form of wikipedia articles with videos illustrating solutions described in the text. The items of the gallery will be presented during the planned public lectures.

Table-top tank for water waves

Realization of a table-top size tank equipped with surface and possibly internal waves generators. This will make possible to perform small scale experiments aimed at popularizing our research.

Publikacje

Soliton Shielding of the Focusing Nonlinear Schrödinger Equation

Autorzy: Marco Bertola, Tamara Grava, and Giuseppe Orsatti
Opublikowane w: Physical Review Letters, 2023, ISSN 0031-9007
Wydawca: American Physical Society
DOI: 10.1103/physrevlett.130.127201

The sharp quantitative isocapacitary inequality (the case of p-capacity)

Autorzy: Ekaterina Mukoseeva
Opublikowane w: Advances in Calculus of Variations, 2021, ISSN 1864-8258
Wydawca: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2020-0106

Poisson quasi-Nijenhuis deformations of the canonical PN structure

Autorzy: G. Falqui; I. Mencattini; M. Pedroni
Opublikowane w: Journal of Geometry and Physics, 2023, ISSN 0393-0440
Wydawca: Elsevier BV
DOI: 10.1016/j.geomphys.2023.104773

Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

Autorzy: Massimo Gisonni; Tamara Grava; Tamara Grava; Giulio Ruzza; Giulio Ruzza
Opublikowane w: Annales Henri Poincaré, 2020, ISSN 1424-0637
Wydawca: Birkhauser Verlag
DOI: 10.1007/s00023-020-00922-4

Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process

Autorzy: Mattia Cafasso, Giulio Ruzza
Opublikowane w: Journal of the London Mathematical Society, 2023, ISSN 0024-6107
Wydawca: Oxford University Press
DOI: 10.1112/jlms.12745

Rigorous Asymptotics of a KdV Soliton Gas

Autorzy: Manuela Girotti; Tamara Grava; Tamara Grava; Robert Jenkins; Kenneth D.T-R McLaughlin
Opublikowane w: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-021-03942-1

On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data

Autorzy: Tamara Grava and Alexander Minakov
Opublikowane w: SIAM Journal on Mathematical Analysis (SIMA), 2020, ISSN 0036-1410
Wydawca: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1279964

Evolution of interface singularities in shallow water equations with variable bottom topography

Autorzy: R. Camassa, R. D'Onofrio, G. Falqui, G. Ortenzi, M. Pedroni
Opublikowane w: Studies in Applied Mathematics, 2022, ISSN 0022-2526
Wydawca: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12480

Simple two-layer dispersive models in the Hamiltonian reduction formalism

Autorzy: R. Camassa, G. Falqui, M. Pedroni, G. Ortenzi & Vu Ho, T.T.
Opublikowane w: Nonlinearity, 2023, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ace3a0

Entanglement of Two Disjoint Intervals in Conformal Field Theory and the 2D Coulomb Gas on a Lattice.

Autorzy: Tamara Grava; Tamara Grava; Andrew P. Kels; Erik Tonni
Opublikowane w: Physical Review Letters, 2021, ISSN 0031-9007
Wydawca: American Physical Society
DOI: 10.1103/physrevlett.127.141605

Integrable hierarchies, Frölicher–Nijenhuisbicomplexes and Lauricella bi-flat F-manifolds

Autorzy: Paolo Lorenzoni and Sara Perletti
Opublikowane w: Nonlinearity, 2023, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad05dc

Isomonodromic Tau Functions on a Torus as Fredholm Determinants, and Charged Partitions

Autorzy: Fabrizio Del Monte, Harini Desiraju & Pavlo Gavrylenko
Opublikowane w: Communications in Mathematical Physics, 2023, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-022-04458-y

Miura-reciprocal transformations and localizable Poisson pencils

Autorzy: P Lorenzoni; S Shadrin; R Vitolo
Opublikowane w: Nonlinearity, 2024, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad1494

On blowups of vorticity for the homogeneous Euler equation

Autorzy: B. G. Konopelchenko, G. Ortenzi
Opublikowane w: Studies in Applied Mathematics, 2023, ISSN 0022-2526
Wydawca: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12618

Large |k| Behavior of Complex Geometric Optics Solutions to d-bar Problems

Autorzy: Christian Klein, Johannes Sjöstrand, Nikola Stoilov
Opublikowane w: Communications on Pure and Applied Mathematics, 2022, ISSN 0010-3640
Wydawca: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22075

Fredholm determinant representation of the homogeneous Painlevé II τ-function

Autorzy: Harini Desiraju
Opublikowane w: Nonlinearity, 2021, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abf84a

Hamiltonian Aspects of Three-Layer Stratified Fluids

Autorzy: R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni & T. T. Vu Ho
Opublikowane w: Journal of Nonlinear Science, 2021, ISSN 0938-8974
Wydawca: Springer Verlag
DOI: 10.1007/s00332-021-09726-0

Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit

Autorzy: Tamara Grava; Tamara Grava; Alberto Maspero; Guido Mazzuca; Antonio Ponno
Opublikowane w: Communications in Mathematical Physics, 2020, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-020-03866-2

Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel

Autorzy: Thomas Bothner; Mattia Cafasso; Sofia Tarricone
Opublikowane w: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Numer 3, 2022, ISSN 0246-0203
Wydawca: Elsevier BV
DOI: 10.1214/21-aihp1211

On the mean density of states of some matrices related to the beta ensembles and an application to the Toda lattice

Autorzy: Guido Mazzuca
Opublikowane w: Journal of Mathematical Physics, 2022, ISSN 0022-2488
Wydawca: American Institute of Physics
DOI: 10.1063/5.0076539

On the modified fractional Korteweg-de Vries and related equations

Autorzy: Klein, C.; Saut, J. -C.; Wang, Yuexun
Opublikowane w: Nonlinearity, 2022, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac4814

On numerical approaches to nonlinear Schrödinger and Korteweg–de Vries equations for piecewise smooth and slowly decaying initial data

Autorzy: Christian KleinJuan Prada-Malagon, Nikola Stoilov
Opublikowane w: Physica D, 2023, ISSN 0167-2789
Wydawca: Elsevier BV
DOI: 10.1016/j.physd.2023.133885

Tau-functions for the Ablowitz–Ladik hierarchy: the matrix-resolvent method

Autorzy: Mattia Cafasso; Di Yang
Opublikowane w: Journal of Physics A: Mathematical and Theoretical, 2022, ISSN 1751-8113
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac5e74

Discrete Integrable Systems and Random Lax Matrices

Autorzy: Tamara Grava; Massimo Gisonni; Giorgio Gubbiotti; Guido Mazzuca
Opublikowane w: Journal of Statistical Physics, 2022, ISSN 0022-4715
Wydawca: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-022-03024-z

Higher-order degenerations of Fay’s identities and applications to integrable equations

Autorzy: Christian Klein and Jordi Pillet
Opublikowane w: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023, ISSN 1364-5021
Wydawca: Royal Society of London
DOI: 10.1098/rspa.2023.0031

Correlation Functions for a Chain of Short Range Oscillators

Autorzy: Tamara Grava; Tamara Grava; T. Kriecherbauer; Guido Mazzuca; Kenneth D.T-R McLaughlin
Opublikowane w: Journal of Statistical Physics, 2021, ISSN 0022-4715
Wydawca: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-021-02735-z

A Riemann-Hilbert approach to the lower tail of the KPZ equation

Autorzy: Cafasso, Mattia; Claeys, Tom
Opublikowane w: Communications on Pure and Applied Mathematics, 2022, ISSN 0010-3640
Wydawca: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21978

Matrix models for stationary Gromov–Witten invariants of the Riemann sphere

Autorzy: M Bertola and G Ruzza
Opublikowane w: Nonlinearity, 2021, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abd85e

Numerical Approach to Painlevé Transcendents on Unbounded Domains

Autorzy: Christian Klein, Nikola Stoilov
Opublikowane w: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Wydawca: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.068

Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials

Autorzy: Mattia Cafasso, Ann du Crest de Villeneuve, Di Yang
Opublikowane w: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Wydawca: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.104

The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type

Autorzy: Mattia Cafasso, Manuel D. de la Iglesia
Opublikowane w: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Wydawca: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.076

Painlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane

Autorzy: Marco Bertola, José Gustavo Elias Rebelo, Tamara Grava
Opublikowane w: Symmetry, Integrability and Geometry: Methods and Applications, 2018, ISSN 1815-0659
Wydawca: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2018.091

Noncommutative Painlevé Equations and Systems of Calogero Type

Autorzy: M. Bertola, M. Cafasso, V. Rubtsov
Opublikowane w: Communications in Mathematical Physics, Numer 363/2, 2018, Strona(/y) 503-530, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-018-3210-0

Hydrodynamic Models and Confinement Effects by Horizontal Boundaries

Autorzy: R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni, C. Thomson
Opublikowane w: Journal of Nonlinear Science, Numer 29/4, 2019, Strona(/y) 1445-1498, ISSN 0938-8974
Wydawca: Springer Verlag
DOI: 10.1007/s00332-018-9522-6

Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes

Autorzy: Mattia Cafasso, Tom Claeys, Manuela Girotti
Opublikowane w: International Mathematics Research Notices, 2019, ISSN 1073-7928
Wydawca: Oxford University Press
DOI: 10.1093/imrn/rnz168

A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

Autorzy: Estelle Basor, Pavel Bleher, Robert Buckingham, Tamara Grava, Alexander Its, Elizabeth Its, Jonathan P Keating
Opublikowane w: Nonlinearity, Numer 32/10, 2019, Strona(/y) 4033-4078, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab28c7

Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation

Autorzy: Christian Klein, Ken McLaughlin, Nikola Stoilov
Opublikowane w: Physica D: Nonlinear Phenomena, Numer 400, 2019, Strona(/y) 132126, ISSN 0167-2789
Wydawca: Elsevier BV
DOI: 10.1016/j.physd.2019.05.006

Quantum D 4 Drinfeld–Sokolov hierarchy and quantum singularity theory

Autorzy: Ann du Crest de Villeneuve, Paolo Rossi
Opublikowane w: Journal of Geometry and Physics, Numer 141, 2019, Strona(/y) 29-44, ISSN 0393-0440
Wydawca: Elsevier BV
DOI: 10.1016/j.geomphys.2019.02.011

Singularity formation as a wetting mechanism in a dispersionless water wave model

Autorzy: R Camassa, G Falqui, G Ortenzi, M Pedroni, G Pitton
Opublikowane w: Nonlinearity, Numer 32/10, 2019, Strona(/y) 4079-4116, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab2a1a

Multidomain spectral method for the Gauss hypergeometric function

Autorzy: S. Crespo, M. Fasondini, C. Klein, N. Stoilov, C. Vallée
Opublikowane w: Numerical Algorithms, 2019, ISSN 1017-1398
Wydawca: Baltzer Science Publishers B.V.
DOI: 10.1007/s11075-019-00741-7

On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations

Autorzy: Roberto Camassa, Gregorio Falqui, Giovanni Ortenzi, Marco Pedroni
Opublikowane w: Symmetry, Integrability and Geometry: Methods and Applications, 2019, ISSN 1815-0659
Wydawca: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2019.087

Brezin–Gross–Witten tau function and isomonodromic deformations

Autorzy: Marco Bertola, Giulio Ruzza
Opublikowane w: Communications in Number Theory and Physics, Numer 13/4, 2019, Strona(/y) 827-883, ISSN 1931-4523
Wydawca: International Press of Boston, Inc.
DOI: 10.4310/cntp.2019.v13.n4.a4

The τ -function of the Ablowitz-Segur family of solutions to Painlevé II as a Widom constant

Autorzy: Harini Desiraju
Opublikowane w: Journal of Mathematical Physics, Numer 60/11, 2019, Strona(/y) 113505, ISSN 0022-2488
Wydawca: American Institute of Physics
DOI: 10.1063/1.5120357

On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions

Autorzy: Jack Arbunich, Christian Klein, Christof Sparber
Opublikowane w: ESAIM: Mathematical Modelling and Numerical Analysis, Numer 53/5, 2019, Strona(/y) 1477-1505, ISSN 0764-583X
Wydawca: EDP Sciences
DOI: 10.1051/m2an/2019018

Numerical scattering for the defocusing Davey–Stewartson II equation for initial data with compact support

Autorzy: Christian Klein, Nikola Stoilov
Opublikowane w: Nonlinearity, Numer 32/11, 2019, Strona(/y) 4258-4280, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab28c6

A Study of the Direct Spectral Transform for the Defocusing Davey‐Stewartson II Equation the Semiclassical Limit

Autorzy: O. Assainova, C. Klein, K. D. T.‐R. McLaughlin, P. D. Miller
Opublikowane w: Communications on Pure and Applied Mathematics, Numer 72/7, 2019, Strona(/y) 1474-1547, ISSN 0010-3640
Wydawca: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21822

On the “Vacuum” Dam-Break Problem: Exact Solutions and Their Long Time Asymptotics

Autorzy: Roberto Camassa, Gregorio Falqui, Giovanni Ortenzi, Marco Pedroni, Giuseppe Pitton
Opublikowane w: SIAM Journal on Applied Mathematics, Numer 80/1, 2020, Strona(/y) 44-70, ISSN 0036-1399
Wydawca: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1266836

Borodin–Okounkov formula, string equation and topological solutions of Drinfeld–Sokolov hierarchies

Autorzy: Mattia Cafasso, Chao-Zhong Wu
Opublikowane w: Letters in Mathematical Physics, Numer 109/12, 2019, Strona(/y) 2681-2722, ISSN 0377-9017
Wydawca: Kluwer Academic Publishers
DOI: 10.1007/s11005-019-01205-8

Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds

Autorzy: P. Lorenzoni, R. Vitolo
Opublikowane w: Journal of Geometry and Physics, Numer 149, 2020, Strona(/y) 103573, ISSN 0393-0440
Wydawca: Elsevier BV
DOI: 10.1016/j.geomphys.2019.103573

Three computational approaches to weakly nonlocal Poisson brackets

Autorzy: Matteo Casati, Paolo Lorenzoni, Raffaele Vitolo
Opublikowane w: Studies in Applied Mathematics, 2020, ISSN 0022-2526
Wydawca: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12302

Tau Functions as Widom Constants

Autorzy: M. Cafasso, P. Gavrylenko, O. Lisovyy
Opublikowane w: Communications in Mathematical Physics, Numer 365/2, 2019, Strona(/y) 741-772, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-018-3230-9

The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain

Autorzy: Peter J. Forrester; G. Mazzuca
Opublikowane w: Journal of Mathematical Physics, 2021, ISSN 0022-2488
Wydawca: American Institute of Physics
DOI: 10.1063/5.0048481

Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Autorzy: Massimo Gisonni, Tamara Grava & Giulio Ruzza
Opublikowane w: Letters in Mathematical Physics, 2021, ISSN 0377-9017
Wydawca: Kluwer Academic Publishers
DOI: 10.1007/s11005-021-01396-z

Failure of scattering for the NLSE with a point interaction in dimension two and three

Autorzy: Claudio Cacciapuoti; Domenico Finco; Diego Noja
Opublikowane w: Nonlinearity, 2023, ISSN 0951-7715
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6544/acf1ee

Airy Kernel Determinant Solutions to the KdV Equation and Integro-Differential Painlevé Equations

Autorzy: Mattia Cafasso; Tom Claeys; Giulio Ruzza
Opublikowane w: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-021-04108-9

Multidomain spectral approach to rational-order fractional derivatives

Autorzy: Klein, Christian, Stoilov, Nikola
Opublikowane w: Studies in Applied Mathematics, 2024, ISSN 0022-2526
Wydawca: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12671

Numerical study of Davey–Stewartson I systems

Autorzy: Jörg Frauendiener, Christian Klein, Umar Muhammad, Nikola Stoilov
Opublikowane w: Studies in applied mathematics, 2022, ISSN 0022-2526
Wydawca: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12491

On the spectral problem of the quantum KdV hierarchy

Autorzy: Giulio Ruzza and Di Yang
Opublikowane w: Journal of Physics A: Mathematical and Theoretical, 2021, ISSN 1751-8113
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac190a

Poisson Quasi-Nijenhuis Manifolds and the Toda System

Autorzy: Gregorio Falqui; Igor Mencattini; Giovanni Ortenzi; Marco Pedroni
Opublikowane w: Mathematical Physics, Analysis and Geometry, 2020, ISSN 1385-0172
Wydawca: Kluwer Academic Publishers
DOI: 10.1007/s11040-020-09352-4

Solutions and singularities of the semigeostrophic equations via the geometry of Lagrangian submanifolds

Autorzy: Roberto D’Onofrio; Giovanni Ortenzi; Ian Roulstone; Volodya Rubtsov
Opublikowane w: Proceedings of the Royal Society A, 2023, ISSN 1364-5021
Wydawca: Royal Society of London
DOI: 10.1098/rspa.2022.0682

Generalized Gibbs Ensemble of the Ablowitz–Ladik Lattice, Circular β-Ensemble and Double Confluent Heun Equation

Autorzy: Tamara Grava & Guido Mazzuca
Opublikowane w: Communications in Mathematical Physics, 2023, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-023-04642-8

Well posedness of the nonlinear Schrödinger equation with isolated singularities

Autorzy: Claudio Cacciapuoti; Domenico Finco; Diego Noja
Opublikowane w: Journal of Differential Equations, 2021, ISSN 0022-0396
Wydawca: Academic Press
DOI: 10.1016/j.jde.2021.10.017

Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies

Autorzy: Alessandro Arsie; Alexandr Buryak; Alexandr Buryak; Alexandr Buryak; Paolo Lorenzoni; Paolo Lorenzoni; Paolo Rossi
Opublikowane w: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Wydawca: Springer Verlag
DOI: 10.1007/s00220-021-04109-8

Numerical study of fractional Camassa–Holm equations

Autorzy: Christian Klein; Goksu Oruc
Opublikowane w: Physica D, 2024, ISSN 0167-2789
Wydawca: Elsevier BV
DOI: 10.1016/j.physd.2023.133979

Stable vector bundles on the families of curves

Autorzy: Fedor Bogomolov, Elena Lukzen
Opublikowane w: European Journal of Mathematics, 2022, ISSN 2199-675X
Wydawca: Springer Nature
DOI: 10.1007/s40879-021-00527-z

Isomonodromic Laplace transform with coalescing eigenvalues and confluence of Fuchsian singularities

Autorzy: Davide Guzzetti
Opublikowane w: Letters in Mathematical Physics, 2021, ISSN 0377-9017
Wydawca: Kluwer Academic Publishers
DOI: 10.1007/s11005-021-01423-z

Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics

Autorzy: Alessandro Arsie; Alexandr Buryak; Alexandr Buryak; Alexandr Buryak; Paolo Lorenzoni; Paolo Lorenzoni; Paolo Rossi
Opublikowane w: International Mathematics Research Notices, 2021, ISSN 1073-7928
Wydawca: Oxford University Press
DOI: 10.1093/imrn/rnab203

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