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
Cuccagna, Scipio; Maeda, Masaya Revisiting asymptotic stability of solitons of nonlinear Schrödinger equations via refined profile method. (English) Zbl 1490.35406 J. Evol. Equ. 22, No. 2, Paper No. 51, 27 p. (2022). MSC: 35Q55 35Q41 35C08 35B40 35B35 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, J. Evol. Equ. 22, No. 2, Paper No. 51, 27 p. (2022; Zbl 1490.35406) Full Text: DOI arXiv
Zhang, Jingxuan A generic framework of adiabatic approximation for nonlinear evolutions. (English) Zbl 1502.37084 Lett. Math. Phys. 112, No. 2, Paper No. 31, 34 p. (2022). MSC: 37L65 37L05 37L25 37K06 37K40 PDFBibTeX XMLCite \textit{J. Zhang}, Lett. Math. Phys. 112, No. 2, Paper No. 31, 34 p. (2022; Zbl 1502.37084) Full Text: DOI arXiv
Gallo, Marco Multiplicity and concentration results for local and fractional NLS equations with critical growth. (English) Zbl 1487.35034 Adv. Differ. Equ. 26, No. 9-10, 397-424 (2021). Reviewer: Christos Sourdis (Athína) MSC: 35B25 35B33 35B40 35J61 35R11 47J30 58E05 PDFBibTeX XMLCite \textit{M. Gallo}, Adv. Differ. Equ. 26, No. 9--10, 397--424 (2021; Zbl 1487.35034) Full Text: arXiv Euclid
Cuccagna, Scipio; Maeda, Masaya A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II. (English) Zbl 1475.35313 Discrete Contin. Dyn. Syst., Ser. S 14, No. 5, 1693-1716 (2021). MSC: 35Q55 35B40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 5, 1693--1716 (2021; Zbl 1475.35313) Full Text: DOI arXiv
Mashkin, Timur Invariant manifold of modified solitons for the perturbed sine-Gordon equation. (English) Zbl 1479.35746 Nonlinearity 34, No. 10, 6930-6962 (2021). MSC: 35Q53 35L70 35C08 35B20 35A24 35R01 PDFBibTeX XMLCite \textit{T. Mashkin}, Nonlinearity 34, No. 10, 6930--6962 (2021; Zbl 1479.35746) Full Text: DOI
Mashkin, Timur Solitons in the presence of a small, slowly varying perturbation. (English) Zbl 1448.35450 Appl. Anal. 99, No. 13, 2258-2279 (2020). MSC: 35Q53 35L70 35C08 53D05 PDFBibTeX XMLCite \textit{T. Mashkin}, Appl. Anal. 99, No. 13, 2258--2279 (2020; Zbl 1448.35450) Full Text: DOI arXiv
Mashkin, Timur Stability of the solitary manifold of the perturbed sine-Gordon equation. (English) Zbl 1442.35065 J. Math. Anal. Appl. 486, No. 2, Article ID 123904, 37 p. (2020). MSC: 35C08 35L71 35B40 PDFBibTeX XMLCite \textit{T. Mashkin}, J. Math. Anal. Appl. 486, No. 2, Article ID 123904, 37 p. (2020; Zbl 1442.35065) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya Long time oscillation of solutions of nonlinear Schrödinger equations near minimal mass ground state. (English) Zbl 1439.35439 J. Differ. Equations 268, No. 10, 6416-6480 (2020). MSC: 35Q55 35B06 35B05 35B40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, J. Differ. Equations 268, No. 10, 6416--6480 (2020; Zbl 1439.35439) Full Text: DOI arXiv
Bambusi, D.; Maspero, A. Freezing of energy of a soliton in an external potential. (English) Zbl 1342.35320 Commun. Math. Phys. 344, No. 1, 155-191 (2016). MSC: 35Q55 35C08 PDFBibTeX XMLCite \textit{D. Bambusi} and \textit{A. Maspero}, Commun. Math. Phys. 344, No. 1, 155--191 (2016; Zbl 1342.35320) Full Text: DOI arXiv
Poncet, Romain; Fukuizumi, Reika; Bouard, Anne de Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time. (English) Zbl 1325.35205 Discrete Contin. Dyn. Syst., Ser. B 20, No. 9, 2793-2817 (2015). MSC: 35Q55 60H15 82B26 35Q84 PDFBibTeX XMLCite \textit{R. Poncet} et al., Discrete Contin. Dyn. Syst., Ser. B 20, No. 9, 2793--2817 (2015; Zbl 1325.35205) Full Text: DOI
Bonanno, Claudio Long time dynamics of highly concentrated solitary waves for the nonlinear Schrödinger equation. (English) Zbl 1304.35632 J. Differ. Equations 258, No. 3, 717-735 (2015). MSC: 35Q55 35Q51 35C08 PDFBibTeX XMLCite \textit{C. Bonanno}, J. Differ. Equations 258, No. 3, 717--735 (2015; Zbl 1304.35632) Full Text: DOI arXiv
Babin, Anatoli; Figotin, Alexander Newton’s law for a trajectory of concentration of solutions to nonlinear Schrödinger equation. (English) Zbl 1304.35631 Commun. Pure Appl. Anal. 13, No. 5, 1685-1718 (2014). MSC: 35Q55 35Q60 35Q70 70S05 78A35 35B40 83C05 PDFBibTeX XMLCite \textit{A. Babin} and \textit{A. Figotin}, Commun. Pure Appl. Anal. 13, No. 5, 1685--1718 (2014; Zbl 1304.35631) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya On weak interaction between a ground state and a non-trapping potential. (English) Zbl 1285.35107 J. Differ. Equations 256, No. 4, 1395-1466 (2014). MSC: 35Q55 35Q51 35B35 35B40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, J. Differ. Equations 256, No. 4, 1395--1466 (2014; Zbl 1285.35107) Full Text: DOI arXiv
Babin, Anatoli; Figotin, Alexander Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation. (English) Zbl 1272.83010 Commun. Math. Phys. 322, No. 2, 453-499 (2013). MSC: 83C05 35L05 83A05 83C40 PDFBibTeX XMLCite \textit{A. Babin} and \textit{A. Figotin}, Commun. Math. Phys. 322, No. 2, 453--499 (2013; Zbl 1272.83010) Full Text: DOI arXiv
Benci, Vieri; Ghimenti, Marco; Micheletti, Anna Maria On the dynamics of solitons in the nonlinear Schrödinger equation. (English) Zbl 1256.35129 Arch. Ration. Mech. Anal. 205, No. 2, 467-492 (2012). MSC: 35Q55 35Q51 35C08 PDFBibTeX XMLCite \textit{V. Benci} et al., Arch. Ration. Mech. Anal. 205, No. 2, 467--492 (2012; Zbl 1256.35129) Full Text: DOI arXiv
Carles, Rémi Interaction of coherent states for Hartree equations. (English) Zbl 1256.35098 Arch. Ration. Mech. Anal. 204, No. 2, 559-598 (2012). MSC: 35Q40 81R30 PDFBibTeX XMLCite \textit{R. Carles}, Arch. Ration. Mech. Anal. 204, No. 2, 559--598 (2012; Zbl 1256.35098) Full Text: DOI arXiv
Muñoz, Claudio Inelastic character of solitons of slowly varying gKdV equations. (English) Zbl 1308.35253 Commun. Math. Phys. 314, No. 3, 817-852 (2012). MSC: 35Q53 35C08 PDFBibTeX XMLCite \textit{C. Muñoz}, Commun. Math. Phys. 314, No. 3, 817--852 (2012; Zbl 1308.35253) Full Text: DOI arXiv
Muñoz, Claudio On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations. (English) Zbl 1291.35264 Math. Ann. 353, No. 3, 867-943 (2012). Reviewer: Yvan Martel (Palaiseau) MSC: 35Q51 35Q53 37K10 37K40 PDFBibTeX XMLCite \textit{C. Muñoz}, Math. Ann. 353, No. 3, 867--943 (2012; Zbl 1291.35264) Full Text: DOI arXiv
Carles, Rémi; Fermanian-Kammerer, Clotilde Nonlinear coherent states and Ehrenfest time for Schrödinger equation. (English) Zbl 1210.35227 Commun. Math. Phys. 301, No. 2, 443-472 (2011). MSC: 35Q55 35A21 81Q20 81V80 PDFBibTeX XMLCite \textit{R. Carles} and \textit{C. Fermanian-Kammerer}, Commun. Math. Phys. 301, No. 2, 443--472 (2011; Zbl 1210.35227) Full Text: DOI arXiv
Benci, Vieri; Ghimenti, Marco; Micheletti, Anna Maria The nonlinear Schrödinger equation: solitons dynamics. (English) Zbl 1205.35287 J. Differ. Equations 249, No. 12, 3312-3341 (2010). MSC: 35Q55 35Q51 37K40 37K45 47J35 PDFBibTeX XMLCite \textit{V. Benci} et al., J. Differ. Equations 249, No. 12, 3312--3341 (2010; Zbl 1205.35287) Full Text: DOI arXiv
Abou Salem, W. K.; Fröhlich, J.; Sigal, I. M. Colliding solitons for the nonlinear Schrödinger equation. (English) Zbl 1184.35289 Commun. Math. Phys. 291, No. 1, 151-176 (2009). MSC: 35Q55 37K40 81Q05 35Q51 35C08 PDFBibTeX XMLCite \textit{W. K. Abou Salem} et al., Commun. Math. Phys. 291, No. 1, 151--176 (2009; Zbl 1184.35289) Full Text: DOI arXiv
Squassina, Marco Soliton dynamics for the nonlinear Schrödinger equation with magnetic field. (English) Zbl 1179.81066 Manuscr. Math. 130, No. 4, 461-494 (2009). MSC: 81Q05 35Q40 35Q51 35Q55 37K40 37K45 PDFBibTeX XMLCite \textit{M. Squassina}, Manuscr. Math. 130, No. 4, 461--494 (2009; Zbl 1179.81066) Full Text: DOI arXiv
Long, Eamonn; Stuart, David Effective dynamics for solitons in the nonlinear Klein-Gordon-Maxwell system and the Lorentz force law. (English) Zbl 1178.35322 Rev. Math. Phys. 21, No. 4, 459-510 (2009). Reviewer: Igor Andrianov (Köln) MSC: 35Q51 35Q60 35Q75 37K40 78A40 PDFBibTeX XMLCite \textit{E. Long} and \textit{D. Stuart}, Rev. Math. Phys. 21, No. 4, 459--510 (2009; Zbl 1178.35322) Full Text: DOI arXiv
Abou Salem, Walid K. Solitary wave dynamics in time-dependent potentials. (English) Zbl 1153.81428 J. Math. Phys. 49, No. 3, 032101, 29 p. (2008). MSC: 35Q55 35Q51 37K40 PDFBibTeX XMLCite \textit{W. K. Abou Salem}, J. Math. Phys. 49, No. 3, 032101, 29 p. (2008; Zbl 1153.81428) Full Text: DOI arXiv
Babin, Anatoli; Figotin, Alexander Nonlinear dynamics of a system of particle-like wavepackets. (English) Zbl 1260.35176 Bardos, Claude (ed.) et al., Instability in models connected with fluid flows I. New York, NY: Springer (ISBN 978-0-387-75216-7/hbk). International Mathematical Series (New York) 6, 53-134 (2008). MSC: 35Q53 35L70 35L75 35L90 PDFBibTeX XMLCite \textit{A. Babin} and \textit{A. Figotin}, Int. Math. Ser., N.Y. 6, 53--134 (2008; Zbl 1260.35176) Full Text: DOI arXiv
Dejak, S. I.; Jonsson, B. L. G. Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves. (English) Zbl 1112.35136 J. Math. Phys. 47, No. 7, 072703, 16 p. (2006). MSC: 35Q53 35Q51 37K40 PDFBibTeX XMLCite \textit{S. I. Dejak} and \textit{B. L. G. Jonsson}, J. Math. Phys. 47, No. 7, 072703, 16 p. (2006; Zbl 1112.35136) Full Text: DOI arXiv