Martel, Yvan; Naumkin, Ivan Nonflat conformal blow-up profiles for the 1-dimensional critical nonlinear Schrödinger equation. (English) Zbl 1527.35387 Tunis. J. Math. 5, No. 3, 505-572 (2023). MSC: 35Q55 35Q41 35B44 35B40 35C08 37K40 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{I. Naumkin}, Tunis. J. Math. 5, No. 3, 505--572 (2023; Zbl 1527.35387) Full Text: DOI
Martel, Yvan; Pilod, Didier Full family of flattening solitary waves for the critical generalized KdV equation. (English) Zbl 1446.35176 Commun. Math. Phys. 378, No. 2, 1011-1080 (2020). MSC: 35Q53 35C08 35B40 35B44 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{D. Pilod}, Commun. Math. Phys. 378, No. 2, 1011--1080 (2020; Zbl 1446.35176) Full Text: DOI arXiv
Martel, Yvan; Raphaël, Pierre Strongly interacting blow up bubbles for the mass critical nonlinear Schrödinger equation. (English. French summary) Zbl 1403.35280 Ann. Sci. Éc. Norm. Supér. (4) 51, No. 3, 701-737 (2018). MSC: 35Q55 35B44 37K40 35C08 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{P. Raphaël}, Ann. Sci. Éc. Norm. Supér. (4) 51, No. 3, 701--737 (2018; Zbl 1403.35280) Full Text: Link
Côte, Raphaël; Martel, Yvan Multi-travelling waves for the nonlinear Klein-Gordon equation. (English) Zbl 1403.35260 Trans. Am. Math. Soc. 370, No. 10, 7461-7487 (2018); corrigendum ibid. 375, No. 5, 3755-3757 (2022). Reviewer: Joseph Shomberg (Providence) MSC: 35Q51 35L71 35Q40 35B20 PDFBibTeX XMLCite \textit{R. Côte} and \textit{Y. Martel}, Trans. Am. Math. Soc. 370, No. 10, 7461--7487 (2018; Zbl 1403.35260) Full Text: DOI arXiv
Martel, Yvan; Pilod, Didier Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation. (English) Zbl 1391.35077 Math. Ann. 369, No. 1-2, 153-245 (2017). MSC: 35B44 35R09 35Q53 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{D. Pilod}, Math. Ann. 369, No. 1--2, 153--245 (2017; Zbl 1391.35077) Full Text: DOI arXiv
Combet, Vianney; Martel, Yvan Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation. (English) Zbl 1423.35334 Bull. Sci. Math. 141, No. 2, 20-103 (2017). MSC: 35Q53 35B44 35B40 35C20 PDFBibTeX XMLCite \textit{V. Combet} and \textit{Y. Martel}, Bull. Sci. Math. 141, No. 2, 20--103 (2017; Zbl 1423.35334) Full Text: DOI arXiv
Le Coz, Stefan; Martel, Yvan; Raphaël, Pierre Minimal mass blow up solutions for a double power nonlinear Schrödinger equation. (English) Zbl 1354.35141 Rev. Mat. Iberoam. 32, No. 3, 795-833 (2016). MSC: 35Q55 35B44 35B33 PDFBibTeX XMLCite \textit{S. Le Coz} et al., Rev. Mat. Iberoam. 32, No. 3, 795--833 (2016; Zbl 1354.35141) Full Text: DOI arXiv
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre Codimension one threshold manifold for the critical gKdV equation. (English) Zbl 1336.35315 Commun. Math. Phys. 342, No. 3, 1075-1106 (2016). MSC: 35Q53 35C08 35B44 PDFBibTeX XMLCite \textit{Y. Martel} et al., Commun. Math. Phys. 342, No. 3, 1075--1106 (2016; Zbl 1336.35315) Full Text: DOI arXiv
Martel, Yvan; Merle, Frank; Raphaël, Pierre Blow up for the critical gKdV equation. II: Minimal mass dynamics. (English) Zbl 1326.35320 J. Eur. Math. Soc. (JEMS) 17, No. 8, 1855-1925 (2015). Reviewer: Ahmed Lesfari (El Jadida) MSC: 35Q53 35B44 35B40 35A02 35B41 35C08 PDFBibTeX XMLCite \textit{Y. Martel} et al., J. Eur. Math. Soc. (JEMS) 17, No. 8, 1855--1925 (2015; Zbl 1326.35320) Full Text: DOI arXiv
Martel, Yvan; Merle, Frank; Raphaël, Pierre Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. (English) Zbl 1301.35137 Acta Math. 212, No. 1, 59-140 (2014). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q53 35Q51 35B44 35C08 PDFBibTeX XMLCite \textit{Y. Martel} et al., Acta Math. 212, No. 1, 59--140 (2014; Zbl 1301.35137) Full Text: DOI
Martel, Yvan; Merle, Frank; Raphaël, Pierre Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. (English) Zbl 1319.35224 Sémin. Laurent Schwartz, EDP Appl. 2011-2012, Exp. No. XXXVII, 14 p. (2013). MSC: 35Q53 35B44 35Q51 35C08 PDFBibTeX XMLCite \textit{Y. Martel} et al., Sémin. Laurent Schwartz, EDP Appl. 2011--2012, Exp. No. XXXVII, 14 p. (2013; Zbl 1319.35224) Full Text: DOI arXiv
Krieger, Joachim; Raphaël, Pierre; Martel, Yvan Two-soliton solutions to the three-dimensional gravitational Hartree equation. (English) Zbl 1193.35163 Commun. Pure Appl. Math. 62, No. 11, 1501-1550 (2009). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35Q40 35Q51 35B40 70F05 83C50 35C05 PDFBibTeX XMLCite \textit{J. Krieger} et al., Commun. Pure Appl. Math. 62, No. 11, 1501--1550 (2009; Zbl 1193.35163) Full Text: DOI arXiv
Kenig, Carlos E.; Martel, Yvan Global well-posedness in the energy space for a modified KP II equation via the Miura transform. (English) Zbl 1106.35082 Trans. Am. Math. Soc. 358, No. 6, 2447-2488 (2006). Reviewer: Andrew Pickering (Madrid) MSC: 35Q53 37K10 35G25 PDFBibTeX XMLCite \textit{C. E. Kenig} and \textit{Y. Martel}, Trans. Am. Math. Soc. 358, No. 6, 2447--2488 (2006; Zbl 1106.35082) Full Text: DOI
Martel, Yvan; Merle, Frank Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. (English) Zbl 1033.35102 Duke Math. J. 115, No. 2, 385-408 (2002). Reviewer: Messoud Efendiev (Berlin) MSC: 35Q53 35B33 35B40 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, Duke Math. J. 115, No. 2, 385--408 (2002; Zbl 1033.35102) Full Text: DOI
Martel, Yvan; Merle, Frank Blow up in finite time and dynamics of blow up solutions for the \(L^2\)-critical generalized KdV equation. (English) Zbl 0996.35064 J. Am. Math. Soc. 15, No. 3, 617-664 (2002). Reviewer: Igor Andrianov (Köln) MSC: 35Q53 35B40 37K40 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, J. Am. Math. Soc. 15, No. 3, 617--664 (2002; Zbl 0996.35064) Full Text: DOI