Oh, Tadahiro; Quastel, Jeremy; Sosoe, Philippe Global dynamics for the stochastic KdV equation with white noise as initial data. (English) Zbl 07814398 Trans. Am. Math. Soc., Ser. B 11, 420-460 (2024). MSC: 35Q53 35R60 60H30 60H40 35A01 35A02 35R06 PDFBibTeX XMLCite \textit{T. Oh} et al., Trans. Am. Math. Soc., Ser. B 11, 420--460 (2024; Zbl 07814398) Full Text: DOI arXiv
Isom, Bradley; Mantzavinos, Dionyssios; Stefanov, Atanas Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrödinger equation. (English) Zbl 07808053 Math. Ann. 388, No. 3, 2289-2329 (2024). MSC: 35Q55 35B65 35B10 35A01 35A02 PDFBibTeX XMLCite \textit{B. Isom} et al., Math. Ann. 388, No. 3, 2289--2329 (2024; Zbl 07808053) Full Text: DOI arXiv
Banica, Valeria; Lucà, Renato; Tzvetkov, Nikolay; Vega, Luis Blow-up for the 1D cubic NLS. (English) Zbl 07798463 Commun. Math. Phys. 405, No. 1, Paper No. 11, 21 p. (2024). MSC: 35Q55 35Q41 35B44 35B05 35B40 PDFBibTeX XMLCite \textit{V. Banica} et al., Commun. Math. Phys. 405, No. 1, Paper No. 11, 21 p. (2024; Zbl 07798463) Full Text: DOI arXiv
Killip, Rowan; Ntekoume, Maria; Vişan, Monica On the well-posedness problem for the derivative nonlinear Schrödinger equation. (English) Zbl 1522.35470 Anal. PDE 16, No. 5, 1245-1270 (2023). MSC: 35Q55 35Q41 35A01 35A02 37K10 PDFBibTeX XMLCite \textit{R. Killip} et al., Anal. PDE 16, No. 5, 1245--1270 (2023; Zbl 1522.35470) Full Text: DOI arXiv
Chapouto, Andreia A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces. (English) Zbl 1522.35438 J. Dyn. Differ. Equations 35, No. 3, 2537-2578 (2023). MSC: 35Q53 35A01 35A02 35B65 35R25 PDFBibTeX XMLCite \textit{A. Chapouto}, J. Dyn. Differ. Equations 35, No. 3, 2537--2578 (2023; Zbl 1522.35438) Full Text: DOI arXiv
Moşincat, Răzvan; Pilod, Didier Unconditional uniqueness for the Benjamin-Ono equation. (English) Zbl 1518.35012 Pure Appl. Anal. 5, No. 2, 285-322 (2023). MSC: 35A02 35Q53 76B55 PDFBibTeX XMLCite \textit{R. Moşincat} and \textit{D. Pilod}, Pure Appl. Anal. 5, No. 2, 285--322 (2023; Zbl 1518.35012) Full Text: DOI arXiv
Killip, Rowan; Ouyang, Zhimeng; Visan, Monica; Wu, Lei Continuum limit for the Ablowitz-Ladik system. (English) Zbl 1517.35207 Nonlinearity 36, No. 7, 3751-3775 (2023). MSC: 35Q55 37K06 37K10 37K60 PDFBibTeX XMLCite \textit{R. Killip} et al., Nonlinearity 36, No. 7, 3751--3775 (2023; Zbl 1517.35207) Full Text: DOI arXiv
Koch, Herbert; Liao, Xian Conserved energies for the one dimensional Gross-Pitaevskii equation: low regularity case. (English) Zbl 1515.35253 Adv. Math. 420, Article ID 108996, 61 p. (2023). Reviewer: Jiqiang Zheng (Beijing) MSC: 35Q55 35Q41 37K10 37K15 35B65 35B40 PDFBibTeX XMLCite \textit{H. Koch} and \textit{X. Liao}, Adv. Math. 420, Article ID 108996, 61 p. (2023; Zbl 1515.35253) Full Text: DOI arXiv
Klaus, Friedrich Wellposedness of NLS in modulation spaces. (English) Zbl 1505.35326 J. Fourier Anal. Appl. 29, No. 1, Paper No. 9, 37 p. (2023). MSC: 35Q55 35Q41 37K10 35B65 35A01 35A02 PDFBibTeX XMLCite \textit{F. Klaus}, J. Fourier Anal. Appl. 29, No. 1, Paper No. 9, 37 p. (2023; Zbl 1505.35326) Full Text: DOI arXiv
Christ, Michael (ed.); Müller, Detlef (ed.); Thiele, Christoph (ed.); Vargas, Ana (ed.) Real analysis, harmonic analysis and applications. Abstracts from the workshop held July 3–9, 2022. (English) Zbl 1520.00024 Oberwolfach Rep. 19, No. 3, 1743-1803 (2022). MSC: 00B05 00B25 42-06 42Bxx PDFBibTeX XMLCite \textit{M. Christ} (ed.) et al., Oberwolfach Rep. 19, No. 3, 1743--1803 (2022; Zbl 1520.00024) Full Text: DOI
Banica, Valeria; Vega, Luis Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow. (English) Zbl 1510.35287 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 39, No. 4, 927-946 (2022). MSC: 35Q55 35Q41 35Q31 76B47 35B25 76F99 34A34 53A04 PDFBibTeX XMLCite \textit{V. Banica} and \textit{L. Vega}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 39, No. 4, 927--946 (2022; Zbl 1510.35287) Full Text: DOI arXiv
Ntekoume, Maria Symplectic nonsqueezing for the KdV flow on the line. (English) Zbl 1504.35453 Pure Appl. Anal. 4, No. 3, 401-448 (2022). MSC: 35Q53 35K10 35A01 35A02 35B65 PDFBibTeX XMLCite \textit{M. Ntekoume}, Pure Appl. Anal. 4, No. 3, 401--448 (2022; Zbl 1504.35453) Full Text: DOI arXiv
Chen, Gong; Liu, Jiaqi Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces. (English) Zbl 1497.35418 Forum Math. Sigma 10, Paper No. e66, 52 p. (2022). MSC: 35Q53 35Q55 35Q15 35C20 35B40 35B65 PDFBibTeX XMLCite \textit{G. Chen} and \textit{J. Liu}, Forum Math. Sigma 10, Paper No. e66, 52 p. (2022; Zbl 1497.35418) Full Text: DOI arXiv
Mendelson, Dana; Nahmod, Andrea R.; Pavlović, Nataša; Rosenzweig, Matthew; Staffilani, Gigliola Poisson commuting energies for a system of infinitely many bosons. (English) Zbl 1504.35493 Adv. Math. 406, Article ID 108525, 148 p. (2022). MSC: 35Q55 37K10 37K15 81Q05 81V70 53D17 PDFBibTeX XMLCite \textit{D. Mendelson} et al., Adv. Math. 406, Article ID 108525, 148 p. (2022; Zbl 1504.35493) Full Text: DOI arXiv
Bahouri, Hajer; Perelman, Galina Global well-posedness for the derivative nonlinear Schrödinger equation. (English) Zbl 1496.35350 Invent. Math. 229, No. 2, 639-688 (2022). MSC: 35Q55 37K10 37K15 37K35 35A01 35A02 PDFBibTeX XMLCite \textit{H. Bahouri} and \textit{G. Perelman}, Invent. Math. 229, No. 2, 639--688 (2022; Zbl 1496.35350) Full Text: DOI arXiv
Rosenzweig, Matthew The mean-field limit of the Lieb-Liniger model. (English) Zbl 1490.35445 Discrete Contin. Dyn. Syst. 42, No. 6, 3005-3037 (2022). Reviewer: Johanna Michor (Wien) MSC: 35Q55 35Q40 81T10 81V73 81V70 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{M. Rosenzweig}, Discrete Contin. Dyn. Syst. 42, No. 6, 3005--3037 (2022; Zbl 1490.35445) Full Text: DOI arXiv
Wang, Zhong Isoinertial operators around the KdV multi-solitons. (English) Zbl 1490.35355 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 219, Article ID 112820, 24 p. (2022). MSC: 35Q35 35Q53 35Q51 37K06 37K10 37K15 35C08 PDFBibTeX XMLCite \textit{Z. Wang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 219, Article ID 112820, 24 p. (2022; Zbl 1490.35355) Full Text: DOI
Killip, Rowan; Vişan, Monica Orbital stability of KdV multisolitons in \(H^{-1}\). (English) Zbl 1509.35264 Commun. Math. Phys. 389, No. 3, 1445-1473 (2022). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 37K10 37K35 35C08 PDFBibTeX XMLCite \textit{R. Killip} and \textit{M. Vişan}, Commun. Math. Phys. 389, No. 3, 1445--1473 (2022; Zbl 1509.35264) Full Text: DOI arXiv
Oh, Seungly; Stefanov, Atanas G. Smoothing and growth bound of periodic generalized Korteweg-de Vries equation. (English) Zbl 1492.35279 J. Hyperbolic Differ. Equ. 18, No. 4, 899-930 (2021). MSC: 35Q53 35B65 35Q35 PDFBibTeX XMLCite \textit{S. Oh} and \textit{A. G. Stefanov}, J. Hyperbolic Differ. Equ. 18, No. 4, 899--930 (2021; Zbl 1492.35279) Full Text: DOI arXiv
Bringmann, Bjoern; Killip, Rowan; Visan, Monica Global well-posedness for the fifth-order KdV equation in \(H^{-1}(\mathbb{R})\). (English) Zbl 1493.35089 Ann. PDE 7, No. 2, Paper No. 21, 46 p. (2021). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 35A01 PDFBibTeX XMLCite \textit{B. Bringmann} et al., Ann. PDE 7, No. 2, Paper No. 21, 46 p. (2021; Zbl 1493.35089) Full Text: DOI arXiv
Tang, Xingdong; Xu, Guixiang Microscopic conservation laws for the derivative nonlinear Schrödinger equation. (English) Zbl 1480.35362 Lett. Math. Phys. 111, No. 6, Paper No. 138, 25 p. (2021). Reviewer: Ayman Kachmar (Nabaṭiyya) MSC: 35Q55 81Q15 81T15 PDFBibTeX XMLCite \textit{X. Tang} and \textit{G. Xu}, Lett. Math. Phys. 111, No. 6, Paper No. 138, 25 p. (2021; Zbl 1480.35362) Full Text: DOI arXiv
Chen, Gong; Liu, Jiaqi Soliton resolution for the focusing modified KdV equation. (English) Zbl 1494.35128 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 6, 2005-2071 (2021). Reviewer: Ti-Jun Xiao (Fudan) MSC: 35Q15 35Q53 35C08 35B35 35B40 PDFBibTeX XMLCite \textit{G. Chen} and \textit{J. Liu}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 6, 2005--2071 (2021; Zbl 1494.35128) Full Text: DOI arXiv
Harrop-Griffiths, Benjamin; Killip, Rowan; Vişan, Monica Microscopic conservation laws for integrable lattice models. (English) Zbl 1489.37088 Monatsh. Math. 196, No. 3, 477-504 (2021). MSC: 37K60 39A36 37K10 35Q53 35Q55 35Q51 PDFBibTeX XMLCite \textit{B. Harrop-Griffiths} et al., Monatsh. Math. 196, No. 3, 477--504 (2021; Zbl 1489.37088) Full Text: DOI arXiv
Oh, Tadahiro; Wang, Yuzhao Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces. (English) Zbl 1476.35247 J. Anal. Math. 143, No. 2, 723-762 (2021). MSC: 35Q55 37K10 35A01 35A02 PDFBibTeX XMLCite \textit{T. Oh} and \textit{Y. Wang}, J. Anal. Math. 143, No. 2, 723--762 (2021; Zbl 1476.35247) Full Text: DOI arXiv
Isom, Bradley; Mantzavinos, Dionyssios; Oh, Seungly; Stefanov, Atanas Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle. (English) Zbl 1473.35486 J. Differ. Equations 297, 25-46 (2021). MSC: 35Q53 35B65 PDFBibTeX XMLCite \textit{B. Isom} et al., J. Differ. Equations 297, 25--46 (2021; Zbl 1473.35486) Full Text: DOI arXiv
Oh, Tadahiro; Wang, Yuzhao On global well-posedness of the modified KdV equation in modulation spaces. (English) Zbl 1469.35188 Discrete Contin. Dyn. Syst. 41, No. 6, 2971-2992 (2021). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 35B65 42B99 PDFBibTeX XMLCite \textit{T. Oh} and \textit{Y. Wang}, Discrete Contin. Dyn. Syst. 41, No. 6, 2971--2992 (2021; Zbl 1469.35188) Full Text: DOI arXiv
Chapouto, Andreia A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces. (English) Zbl 1468.35165 Discrete Contin. Dyn. Syst. 41, No. 8, 3915-3950 (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 35Q53 35A01 35A02 PDFBibTeX XMLCite \textit{A. Chapouto}, Discrete Contin. Dyn. Syst. 41, No. 8, 3915--3950 (2021; Zbl 1468.35165) Full Text: DOI arXiv
Koch, Herbert; Liao, Xian Conserved energies for the one dimensional Gross-Pitaevskii equation. (English) Zbl 1455.35236 Adv. Math. 377, Article ID 107467, 84 p. (2021). MSC: 35Q55 35Q53 35A01 35A02 35B65 PDFBibTeX XMLCite \textit{H. Koch} and \textit{X. Liao}, Adv. Math. 377, Article ID 107467, 84 p. (2021; Zbl 1455.35236) Full Text: DOI arXiv
Allaire, Grégoire; Lamacz, Agnes; Rauch, Jeffrey Crime pays; homogenization for long times. (English) Zbl 1497.35030 Sémin. Laurent Schwartz, EDP Appl. 2019-2020, Exp. No. 11, 9 p. (2020). MSC: 35B27 35C20 35L10 PDFBibTeX XMLCite \textit{G. Allaire} et al., Sémin. Laurent Schwartz, EDP Appl. 2019--2020, Exp. No. 11, 9 p. (2020; Zbl 1497.35030) Full Text: DOI
Gérard, Patrick A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. (English) Zbl 1479.35020 Sémin. Laurent Schwartz, EDP Appl. 2019-2020, Exp. No. 8, 19 p. (2020). MSC: 35A22 35G25 35Q35 PDFBibTeX XMLCite \textit{P. Gérard}, Sémin. Laurent Schwartz, EDP Appl. 2019--2020, Exp. No. 8, 19 p. (2020; Zbl 1479.35020) Full Text: DOI
Banica, Valeria; Vega, Luis Evolution of polygonal lines by the binormal flow. (English) Zbl 1462.35279 Ann. PDE 6, No. 1, Paper No. 6, 53 p. (2020). MSC: 35Q35 35Q55 35Q31 53A04 76N06 PDFBibTeX XMLCite \textit{V. Banica} and \textit{L. Vega}, Ann. PDE 6, No. 1, Paper No. 6, 53 p. (2020; Zbl 1462.35279) Full Text: DOI arXiv
Kwon, Soonsik; Oh, Tadahiro; Yoon, Haewon Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line. (English. French summary) Zbl 1454.35346 Ann. Fac. Sci. Toulouse, Math. (6) 29, No. 3, 649-720 (2020). MSC: 35Q55 35Q53 35A01 35A02 35D30 PDFBibTeX XMLCite \textit{S. Kwon} et al., Ann. Fac. Sci. Toulouse, Math. (6) 29, No. 3, 649--720 (2020; Zbl 1454.35346) Full Text: DOI arXiv
Banica, Valeria; Vega, Luis On the energy of critical solutions of the binormal flow. (English) Zbl 1454.35273 Commun. Partial Differ. Equations 45, No. 7, 820-845 (2020). MSC: 35Q35 PDFBibTeX XMLCite \textit{V. Banica} and \textit{L. Vega}, Commun. Partial Differ. Equations 45, No. 7, 820--845 (2020; Zbl 1454.35273) Full Text: DOI arXiv HAL
Schippa, Robert On the existence of periodic solutions to the modified Korteweg-de Vries equation below \(H^{1/2}(\mathbb{T})\). (English) Zbl 1448.35455 J. Evol. Equ. 20, No. 3, 725-776 (2020). MSC: 35Q53 42B37 35A01 35B10 35B45 PDFBibTeX XMLCite \textit{R. Schippa}, J. Evol. Equ. 20, No. 3, 725--776 (2020; Zbl 1448.35455) Full Text: DOI arXiv
Forlano, Justin; Oh, Tadahiro; Wang, Yuzhao Stochastic nonlinear Schrödinger equation with almost space-time white noise. (English) Zbl 1442.35418 J. Aust. Math. Soc. 109, No. 1, 44-67 (2020). MSC: 35Q55 60H30 PDFBibTeX XMLCite \textit{J. Forlano} et al., J. Aust. Math. Soc. 109, No. 1, 44--67 (2020; Zbl 1442.35418) Full Text: DOI arXiv
Oh, Tadahiro; Wang, Yuzhao Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces. (English) Zbl 1447.35300 J. Differ. Equations 269, No. 1, 612-640 (2020). Reviewer: Sevdzhan Hakkaev (Šumen) MSC: 35Q55 35Q53 37K10 35A01 35A02 PDFBibTeX XMLCite \textit{T. Oh} and \textit{Y. Wang}, J. Differ. Equations 269, No. 1, 612--640 (2020; Zbl 1447.35300) Full Text: DOI arXiv
Angelopoulos, Yannis; Killip, Rowan; Visan, Monica Invariant measures for integrable spin chains and an integrable discrete nonlinear Schrödinger equation. (English) Zbl 1433.35352 SIAM J. Math. Anal. 52, No. 1, 135-163 (2020). MSC: 35Q55 35Q51 35Q82 37K10 82C20 82D40 35A30 PDFBibTeX XMLCite \textit{Y. Angelopoulos} et al., SIAM J. Math. Anal. 52, No. 1, 135--163 (2020; Zbl 1433.35352) Full Text: DOI arXiv
Perry, Peter A. Inverse scattering and global well-posedness in one and two space dimensions. (English) Zbl 1442.35429 Miller, Peter D. (ed.) et al., Nonlinear dispersive partial differential equations and inverse scattering. Papers from the focus program on “Nonlinear Dispersive Partial Differential Equations and Inverse Scattering”, Fields Institute, July 31 – August 18, 2017. New York, NY: Springer; Toronto, ON: The Fields Institute for Research in Mathematical Scienes. Fields Inst. Commun. 83, 161-252 (2019). MSC: 35Q55 37K15 35P25 PDFBibTeX XMLCite \textit{P. A. Perry}, Fields Inst. Commun. 83, 161--252 (2019; Zbl 1442.35429) Full Text: DOI arXiv
Killip, Rowan; Vişan, Monica KdV is well-posed in \(H^{-1}\). (English) Zbl 1426.35203 Ann. Math. (2) 190, No. 1, 249-305 (2019). Reviewer: Guido Schneider (Stuttgart) MSC: 35Q53 37K10 35A01 35A02 35B65 PDFBibTeX XMLCite \textit{R. Killip} and \textit{M. Vişan}, Ann. Math. (2) 190, No. 1, 249--305 (2019; Zbl 1426.35203) Full Text: DOI arXiv
Kishimoto, Nobu A remark on norm inflation for nonlinear Schrödinger equations. (English) Zbl 1409.35191 Commun. Pure Appl. Anal. 18, No. 3, 1375-1402 (2019). MSC: 35Q55 35B30 PDFBibTeX XMLCite \textit{N. Kishimoto}, Commun. Pure Appl. Anal. 18, No. 3, 1375--1402 (2019; Zbl 1409.35191) Full Text: DOI arXiv
Banica, Valeria 1-D cubic NLS with several Dirac masses as initial data and consequences. (English) Zbl 1475.35310 Sémin. Laurent Schwartz, EDP Appl. 2017-2018, Exp. No. 3, 9 p. (2018). MSC: 35Q55 PDFBibTeX XMLCite \textit{V. Banica}, Sémin. Laurent Schwartz, EDP Appl. 2017--2018, Exp. No. 3, 9 p. (2018; Zbl 1475.35310) Full Text: DOI
Koch, Herbert; Tataru, Daniel Conserved energies for the cubic nonlinear Schrödinger equation in one dimension. (English) Zbl 1434.35181 Duke Math. J. 167, No. 17, 3207-3313 (2018). Reviewer: Ayman Kachmar (Nabaṭiyya) MSC: 35Q55 37K10 35Q53 16T05 PDFBibTeX XMLCite \textit{H. Koch} and \textit{D. Tataru}, Duke Math. J. 167, No. 17, 3207--3313 (2018; Zbl 1434.35181) Full Text: DOI arXiv Euclid