Chen, Gong; Pusateri, Fabio On the \(1d\) cubic NLS with a non-generic potential. (English) Zbl 07804753 Commun. Math. Phys. 405, No. 2, Paper No. 35, 59 p. (2024). MSC: 35Q55 35B40 35B34 35B65 42A38 35P30 PDFBibTeX XMLCite \textit{G. Chen} and \textit{F. Pusateri}, Commun. Math. Phys. 405, No. 2, Paper No. 35, 59 p. (2024; Zbl 07804753) Full Text: DOI arXiv
Ifrim, Mihaela; Tataru, Daniel Testing by wave packets and modified scattering in nonlinear dispersive PDE’s. (English) Zbl 07803079 Trans. Am. Math. Soc., Ser. B 11, 164-214 (2024). MSC: 35P25 35Q55 76B15 PDFBibTeX XMLCite \textit{M. Ifrim} and \textit{D. Tataru}, Trans. Am. Math. Soc., Ser. B 11, 164--214 (2024; Zbl 07803079) Full Text: DOI arXiv
Lührmann, Jonas; Schlag, Wilhelm Asymptotic stability of the sine-Gordon kink under odd perturbations. (English) Zbl 07783729 Duke Math. J. 172, No. 14, 2715-2820 (2023). Reviewer: Michał Kowalczyk (Santiago de Chile) MSC: 35B35 35C08 35L71 PDFBibTeX XMLCite \textit{J. Lührmann} and \textit{W. Schlag}, Duke Math. J. 172, No. 14, 2715--2820 (2023; Zbl 07783729) Full Text: DOI arXiv Link
Ifrim, Mihaela; Tataru, Daniel Global solutions for 1D cubic defocusing dispersive equations: Part I. (English) Zbl 07781657 Forum Math. Pi 11, Paper No. e31, 46 p. (2023). MSC: 35Q55 35Q41 35B40 35B45 35A01 35A02 PDFBibTeX XMLCite \textit{M. Ifrim} and \textit{D. Tataru}, Forum Math. Pi 11, Paper No. e31, 46 p. (2023; Zbl 07781657) Full Text: DOI arXiv OA License
Liu, Xuan; Zhang, Ting Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime. (English) Zbl 07758698 Nonlinearity 36, No. 12, 6324-6363 (2023). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q55 35Q41 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{X. Liu} and \textit{T. Zhang}, Nonlinearity 36, No. 12, 6324--6363 (2023; Zbl 07758698) Full Text: DOI arXiv
Lindblad, Hans; Schlue, Volker Scattering from infinity for semilinear wave equations satisfying the null condition or the weak null condition. (English) Zbl 1518.35499 J. Hyperbolic Differ. Equ. 20, No. 1, 155-218 (2023). MSC: 35L71 35P25 PDFBibTeX XMLCite \textit{H. Lindblad} and \textit{V. Schlue}, J. Hyperbolic Differ. Equ. 20, No. 1, 155--218 (2023; Zbl 1518.35499) Full Text: DOI arXiv
Kita, Naoyasu; Masaki, Satoshi; Segata, Jun-ichi; Uriya, Kota Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension. (English) Zbl 1510.35305 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 230, Article ID 113216, 22 p. (2023). MSC: 35Q55 35Q41 35A22 35B40 PDFBibTeX XMLCite \textit{N. Kita} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 230, Article ID 113216, 22 p. (2023; Zbl 1510.35305) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya; Scrobogna, Stefano Small energy stabilization for 1D nonlinear Klein Gordon equations. (English) Zbl 1508.35142 J. Differ. Equations 350, 52-88 (2023). MSC: 35Q55 35A01 35A02 35B35 PDFBibTeX XMLCite \textit{S. Cuccagna} et al., J. Differ. Equations 350, 52--88 (2023; Zbl 1508.35142) Full Text: DOI arXiv
Li, Yongming; Lührmann, Jonas Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry. (English) Zbl 1503.35201 J. Differ. Equations 344, 172-202 (2023). MSC: 35Q51 35Q53 35B40 35B35 35B06 35A01 35A02 PDFBibTeX XMLCite \textit{Y. Li} and \textit{J. Lührmann}, J. Differ. Equations 344, 172--202 (2023; Zbl 1503.35201) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya Asymptotic stability of kink with internal modes under odd perturbation. (English) Zbl 1500.35038 NoDEA, Nonlinear Differ. Equ. Appl. 30, No. 1, Paper No. 1, 47 p. (2023). MSC: 35B40 35L71 37K40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, NoDEA, Nonlinear Differ. Equ. Appl. 30, No. 1, Paper No. 1, 47 p. (2023; Zbl 1500.35038) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya On selection of standing wave at small energy in the 1D cubic Schrödinger equation with a trapping potential. (English) Zbl 1503.35208 Commun. Math. Phys. 396, No. 3, 1135-1186 (2022). MSC: 35Q55 35C08 35L71 35B40 37K40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, Commun. Math. Phys. 396, No. 3, 1135--1186 (2022; Zbl 1503.35208) Full Text: DOI arXiv
Aoki, Kazuki; Inui, Takahisa; Miyazaki, Hayato; Mizutani, Haruya; Uriya, Kota Asymptotic behavior for the long-range nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition. (English) Zbl 1501.35361 Pure Appl. Anal. 4, No. 2, 287-311 (2022). MSC: 35Q55 35Q41 35B40 35P25 PDFBibTeX XMLCite \textit{K. Aoki} et al., Pure Appl. Anal. 4, No. 2, 287--311 (2022; Zbl 1501.35361) Full Text: DOI arXiv
Sigal, I. M. Differential equations of quantum mechanics. (English) Zbl 1504.35421 Q. Appl. Math. 80, No. 3, 451-480 (2022). Reviewer: Konstantin Merz (Braunschweig) MSC: 35Q40 35Q41 35Q55 35Q56 81Q99 81U24 81V10 82D55 81V73 81V74 PDFBibTeX XMLCite \textit{I. M. Sigal}, Q. Appl. Math. 80, No. 3, 451--480 (2022; Zbl 1504.35421) Full Text: DOI arXiv
Chen, Gong; Pusateri, Fabio The 1-dimensional nonlinear Schrödinger equation with a weighted \(L^1\) potential. (English) Zbl 1498.35189 Anal. PDE 15, No. 4, 937-982 (2022). Reviewer: Gaetano Siciliano (São Paulo) MSC: 35J10 35P25 35Q55 PDFBibTeX XMLCite \textit{G. Chen} and \textit{F. Pusateri}, Anal. PDE 15, No. 4, 937--982 (2022; Zbl 1498.35189) Full Text: DOI arXiv
Murphy, Jason; Van Hoose, Tim Modified scattering for a dispersion-managed nonlinear Schrödinger equation. (English) Zbl 1483.35220 NoDEA, Nonlinear Differ. Equ. Appl. 29, No. 1, Paper No. 1, 11 p. (2022). MSC: 35Q55 35L71 35P25 PDFBibTeX XMLCite \textit{J. Murphy} and \textit{T. Van Hoose}, NoDEA, Nonlinear Differ. Equ. Appl. 29, No. 1, Paper No. 1, 11 p. (2022; Zbl 1483.35220) Full Text: DOI arXiv
He, Lili Scattering from infinity of the Maxwell Klein Gordon equations in Lorenz gauge. (English) Zbl 1482.35186 Commun. Math. Phys. 386, No. 3, 1747-1801 (2021). MSC: 35Q40 81T13 81Q05 83C22 35B40 35A01 78A45 PDFBibTeX XMLCite \textit{L. He}, Commun. Math. Phys. 386, No. 3, 1747--1801 (2021; Zbl 1482.35186) Full Text: DOI arXiv
Wang, Yuexun Global dynamics of the generalized fifth-order KdV equation with quintic nonlinearity. (English) Zbl 1470.76023 J. Evol. Equ. 21, No. 2, 1449-1475 (2021). MSC: 76B15 35Q35 PDFBibTeX XMLCite \textit{Y. Wang}, J. Evol. Equ. 21, No. 2, 1449--1475 (2021; Zbl 1470.76023) Full Text: DOI arXiv
Lindblad, Hans; Lührmann, Jonas; Soffer, Avy Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities. (English) Zbl 1475.35305 Arch. Ration. Mech. Anal. 241, No. 3, 1459-1527 (2021). MSC: 35Q53 35B40 35B05 35P25 35C08 PDFBibTeX XMLCite \textit{H. Lindblad} et al., Arch. Ration. Mech. Anal. 241, No. 3, 1459--1527 (2021; Zbl 1475.35305) Full Text: DOI arXiv
Lindblad, Hans; Lührmann, Jonas; Soffer, Avy Decay and asymptotics for the one-dimensional Klein-Gordon equation with variable coefficient cubic nonlinearities. (English) Zbl 1455.35021 SIAM J. Math. Anal. 52, No. 6, 6379-6411 (2020). MSC: 35B40 35L71 35L15 35P25 35Q51 35Q56 PDFBibTeX XMLCite \textit{H. Lindblad} et al., SIAM J. Math. Anal. 52, No. 6, 6379--6411 (2020; Zbl 1455.35021) Full Text: DOI arXiv
Uriya, Kota Final state problem for systems of cubic nonlinear Schrödinger equations in one dimension. (English) Zbl 1390.35341 Ann. Henri Poincaré 18, No. 7, 2523-2542 (2017). Reviewer: Andrew Pickering (Madrid) MSC: 35Q55 35B40 35A01 PDFBibTeX XMLCite \textit{K. Uriya}, Ann. Henri Poincaré 18, No. 7, 2523--2542 (2017; Zbl 1390.35341) Full Text: DOI
Ifrim, Mihaela; Tataru, Daniel The lifespan of small data solutions in two dimensional capillary water waves. (English) Zbl 1375.35347 Arch. Ration. Mech. Anal. 225, No. 3, 1279-1346 (2017). MSC: 35Q31 76B45 PDFBibTeX XMLCite \textit{M. Ifrim} and \textit{D. Tataru}, Arch. Ration. Mech. Anal. 225, No. 3, 1279--1346 (2017; Zbl 1375.35347) Full Text: DOI arXiv
Chae, Myeongju; Oh, Sung-Jin Small data global existence and decay for relativistic Chern-Simons equations. (English) Zbl 1383.81134 Ann. Henri Poincaré 18, No. 6, 2123-2198 (2017). Reviewer: Sergiy Koshkin (Houston) MSC: 81T13 70H40 81S22 58J28 PDFBibTeX XMLCite \textit{M. Chae} and \textit{S.-J. Oh}, Ann. Henri Poincaré 18, No. 6, 2123--2198 (2017; Zbl 1383.81134) Full Text: DOI arXiv
Pusateri, Fabio; Murphy, Jason Almost global existence for cubic nonlinear Schrödinger equations in one space dimension. (English) Zbl 1360.35254 Discrete Contin. Dyn. Syst. 37, No. 4, 2077-2102 (2017). MSC: 35Q55 35A01 PDFBibTeX XMLCite \textit{F. Pusateri} and \textit{J. Murphy}, Discrete Contin. Dyn. Syst. 37, No. 4, 2077--2102 (2017; Zbl 1360.35254) Full Text: DOI arXiv
Sagawa, Yuji; Sunagawa, Hideaki The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension. (English) Zbl 1351.35191 Discrete Contin. Dyn. Syst. 36, No. 10, 5743-5761 (2016); corrigendum ibid. 40, No. 7, 4577-4578 (2020). MSC: 35Q55 35B40 PDFBibTeX XMLCite \textit{Y. Sagawa} and \textit{H. Sunagawa}, Discrete Contin. Dyn. Syst. 36, No. 10, 5743--5761 (2016; Zbl 1351.35191) Full Text: DOI arXiv
Hani, Zaher; Thomann, Laurent Asymptotic behavior of the nonlinear Schrödinger equation with harmonic trapping. (English) Zbl 1365.35153 Commun. Pure Appl. Math. 69, No. 9, 1727-1776 (2016). Reviewer: Thomas J. Bartsch (Gießen) MSC: 35Q55 35B40 PDFBibTeX XMLCite \textit{Z. Hani} and \textit{L. Thomann}, Commun. Pure Appl. Math. 69, No. 9, 1727--1776 (2016; Zbl 1365.35153) Full Text: DOI arXiv
Harrop-Griffiths, Benjamin Long time behavior of solutions to the mKdV. (English) Zbl 1342.35303 Commun. Partial Differ. Equations 41, No. 2, 282-317 (2016). MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{B. Harrop-Griffiths}, Commun. Partial Differ. Equations 41, No. 2, 282--317 (2016; Zbl 1342.35303) Full Text: DOI arXiv
Shimomura, Akihiro Asymptotic behavior of solutions for Schrödinger equations with dissipative nonlinearities. (English) Zbl 1105.35118 Commun. Partial Differ. Equations 31, No. 9, 1407-1423 (2006). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35Q55 35B40 81Q05 PDFBibTeX XMLCite \textit{A. Shimomura}, Commun. Partial Differ. Equations 31, No. 9, 1407--1423 (2006; Zbl 1105.35118) Full Text: DOI