Bridges, Thomas J.; Kostianko, Anna; Zelik, Sergey Validity of the hyperbolic Whitham modulation equations in Sobolev spaces. (English) Zbl 07289121 J. Differ. Equations 274, 971-995 (2021). MSC: 35Q55 35Q53 35A01 35A02 PDF BibTeX XML Cite \textit{T. J. Bridges} et al., J. Differ. Equations 274, 971--995 (2021; Zbl 07289121) Full Text: DOI
Bhimani, Divyang G.; Carles, Rémi Norm inflation for nonlinear Schrödinger equations in Fourier-Lebesgue and modulation spaces of negative regularity. (English) Zbl 07296357 J. Fourier Anal. Appl. 26, No. 6, Paper No. 78, 33 p. (2020). MSC: 35Q55 35Q41 42B35 35A01 35B65 35R25 78A05 PDF BibTeX XML Cite \textit{D. G. Bhimani} and \textit{R. Carles}, J. Fourier Anal. Appl. 26, No. 6, Paper No. 78, 33 p. (2020; Zbl 07296357) Full Text: DOI
Sacchetti, Andrea Nonlinear models and bifurcation trees in quantum mechanics: a review of recent results. (English) Zbl 1431.35180 Ric. Mat. 68, No. 2, 883-898 (2019). MSC: 35Q55 81T25 81Q05 35B32 82C10 PDF BibTeX XML Cite \textit{A. Sacchetti}, Ric. Mat. 68, No. 2, 883--898 (2019; Zbl 1431.35180) Full Text: DOI
Kwan, Wingfai; Leung, Shingyu; Wang, Xiao-Ping; Qian, Jianliang A fast Huygens sweeping method for capturing paraxial multi-color optical self-focusing in nematic liquid crystals. (English) Zbl 1380.78001 J. Comput. Phys. 348, 108-138 (2017). MSC: 78A10 78M25 PDF BibTeX XML Cite \textit{W. Kwan} et al., J. Comput. Phys. 348, 108--138 (2017; Zbl 1380.78001) Full Text: DOI
Carles, Rémi; Gallo, Clément On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit. II. Analytic regularity. (English) Zbl 1368.65198 Numer. Math. 136, No. 1, 315-342 (2017). Reviewer: Dana Černá (Liberec) MSC: 65M70 35Q55 65M12 65M15 81Q20 PDF BibTeX XML Cite \textit{R. Carles} and \textit{C. Gallo}, Numer. Math. 136, No. 1, 315--342 (2017; Zbl 1368.65198) Full Text: DOI
Bunoiu, Renata; Precup, Radu; Varga, Csaba Multiple positive standing wave solutions for Schrödinger equations with oscillating state-dependent potentials. (English) Zbl 1362.35281 Commun. Pure Appl. Anal. 16, No. 3, 953-972 (2017). MSC: 35Q55 35J20 47J30 58E05 35B38 35B09 PDF BibTeX XML Cite \textit{R. Bunoiu} et al., Commun. Pure Appl. Anal. 16, No. 3, 953--972 (2017; Zbl 1362.35281) Full Text: DOI
Bao, Weizhu; Le Treust, Loïc; Méhats, Florian Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime. (English) Zbl 1362.35278 Kinet. Relat. Models 10, No. 3, 553-571 (2017). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q55 35B40 PDF BibTeX XML Cite \textit{W. Bao} et al., Kinet. Relat. Models 10, No. 3, 553--571 (2017; Zbl 1362.35278) Full Text: DOI
Balac, Stéphane; Fernandez, Arnaud; Mahé, Fabrice; Méhats, Florian; Texier-Picard, Rozenn The interaction picture method for solving the generalized nonlinear Schrödinger equation in optics. (English) Zbl 1401.78014 ESAIM, Math. Model. Numer. Anal. 50, No. 4, 945-964 (2016). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M25 65M12 65M15 65L06 65T50 78A60 35Q55 PDF BibTeX XML Cite \textit{S. Balac} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 4, 945--964 (2016; Zbl 1401.78014) Full Text: DOI
Balac, Stéphane; Mahé, Fabrice An embedded split-step method for solving the nonlinear Schrödinger equation in optics. (English) Zbl 1349.78088 J. Comput. Phys. 280, 295-305 (2015). MSC: 78M20 65N06 35Q55 35Q60 PDF BibTeX XML Cite \textit{S. Balac} and \textit{F. Mahé}, J. Comput. Phys. 280, 295--305 (2015; Zbl 1349.78088) Full Text: DOI
Li, Xueyang; Xiao, Aiguo Time-splitting finite difference method with the wavelet-adaptive grids for semiclassical Gross-Pitaevskii equation in supercritical case. (English) Zbl 1349.82033 J. Comput. Phys. 267, 146-161 (2014). MSC: 82C10 82C80 65M06 PDF BibTeX XML Cite \textit{X. Li} and \textit{A. Xiao}, J. Comput. Phys. 267, 146--161 (2014; Zbl 1349.82033) Full Text: DOI
Figalli, A.; Klein, C.; Markowich, P.; Sparber, C. WKB analysis of Bohmian dynamics. (English) Zbl 1341.35139 Commun. Pure Appl. Math. 67, No. 4, 581-620 (2014). MSC: 35Q41 35Q40 81Q05 81Q65 35B40 PDF BibTeX XML Cite \textit{A. Figalli} et al., Commun. Pure Appl. Math. 67, No. 4, 581--620 (2014; Zbl 1341.35139) Full Text: DOI arXiv
Lin, Chi-Kun; Segata, Jun-ichi WKB analysis of the Schrödinger-KdV system. (English) Zbl 1294.35123 J. Differ. Equations 256, No. 11, 3817-3834 (2014). Reviewer: Ahmed Lesfari (El Jadida) MSC: 35Q53 35L60 PDF BibTeX XML Cite \textit{C.-K. Lin} and \textit{J.-i. Segata}, J. Differ. Equations 256, No. 11, 3817--3834 (2014; Zbl 1294.35123) Full Text: DOI
Achdou, Yves; Camilli, Fabio; Corrias, Lucilla On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations. (English) Zbl 1282.65105 Discrete Contin. Dyn. Syst., Ser. B 19, No. 3, 629-650 (2014). MSC: 65M12 35F25 35R05 49L25 PDF BibTeX XML Cite \textit{Y. Achdou} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 3, 629--650 (2014; Zbl 1282.65105) Full Text: DOI arXiv
Antoine, Xavier; Bao, Weizhu; Besse, Christophe Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. (English) Zbl 1344.35130 Comput. Phys. Commun. 184, No. 12, 2621-2633 (2013). MSC: 35Q55 65M70 65M06 35Q82 PDF BibTeX XML Cite \textit{X. Antoine} et al., Comput. Phys. Commun. 184, No. 12, 2621--2633 (2013; Zbl 1344.35130) Full Text: DOI arXiv
Colucci, Renato; Chacón, Gerardo R.; Vargas, Andrés Dynamics of a Gross-Pitaevskii equation with phenomenological damping. (English) Zbl 1294.35134 Int. J. Differ. Equ. 2013, Article ID 874196, 8 p. (2013). MSC: 35Q55 35B41 PDF BibTeX XML Cite \textit{R. Colucci} et al., Int. J. Differ. Equ. 2013, Article ID 874196, 8 p. (2013; Zbl 1294.35134) Full Text: DOI
Lee, Long; Lyng, Gregory; Vankova, Irena The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation. (English) Zbl 1253.35160 Physica D 241, No. 21, 1767-1781 (2012). MSC: 35Q55 35B20 65M06 PDF BibTeX XML Cite \textit{L. Lee} et al., Physica D 241, No. 21, 1767--1781 (2012; Zbl 1253.35160) Full Text: DOI
Carles, Rémi; Dumas, Eric; Sparber, Christof Geometric optics and instability for NLS and Davey-Stewartson models. (English) Zbl 1273.35248 J. Eur. Math. Soc. (JEMS) 14, No. 6, 1885-1921 (2012). Reviewer: Vincent Lescarret (Gif-sur-Yvette) MSC: 35Q55 35B40 35A01 35B25 78A05 PDF BibTeX XML Cite \textit{R. Carles} et al., J. Eur. Math. Soc. (JEMS) 14, No. 6, 1885--1921 (2012; Zbl 1273.35248) Full Text: DOI arXiv
Potter, Trevor Effective dynamics for \(N\)-solitons of the Gross-Pitaevskii equation. (English) Zbl 1253.35140 J. Nonlinear Sci. 22, No. 3, 351-370 (2012). MSC: 35Q51 65M70 35C08 PDF BibTeX XML Cite \textit{T. Potter}, J. Nonlinear Sci. 22, No. 3, 351--370 (2012; Zbl 1253.35140) Full Text: DOI arXiv
Masaki, Satoshi Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system. (English) Zbl 1231.35236 J. Differ. Equations 251, No. 11, 3028-3062 (2011). Reviewer: Michael Perelmuter (Kyïv) MSC: 35Q55 81Q20 35B40 PDF BibTeX XML Cite \textit{S. Masaki}, J. Differ. Equations 251, No. 11, 3028--3062 (2011; Zbl 1231.35236) 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 PDF BibTeX XML Cite \textit{R. Carles} and \textit{C. Fermanian-Kammerer}, Commun. Math. Phys. 301, No. 2, 443--472 (2011; Zbl 1210.35227) Full Text: DOI arXiv
Wang, W.-M. Spectral methods in PDE. (English) Zbl 1222.35191 Milan J. Math. 78, No. 2, 561-573 (2010). MSC: 35Q55 35B15 35B30 35P05 PDF BibTeX XML Cite \textit{W. M. Wang}, Milan J. Math. 78, No. 2, 561--573 (2010; Zbl 1222.35191) Full Text: DOI
Cordero-Soto, R.; Suslov, S. K. Time reversal for modified oscillators. (English. Russian original) Zbl 1201.81046 Theor. Math. Phys. 162, No. 3, 286-316 (2010); translation from Teor. Mat. Fiz. 162, No. 3, 345-380 (2010). MSC: 81Q05 35Q55 35Q41 35J08 PDF BibTeX XML Cite \textit{R. Cordero-Soto} and \textit{S. K. Suslov}, Theor. Math. Phys. 162, No. 3, 286--316 (2010; Zbl 1201.81046); translation from Teor. Mat. Fiz. 162, No. 3, 345--380 (2010) Full Text: DOI
Markowich, Peter; Paul, Thierry; Sparber, Christof Bohmian measures and their classical limit. (English) Zbl 1195.81060 J. Funct. Anal. 259, No. 6, 1542-1576 (2010). MSC: 81Q20 81Q65 PDF BibTeX XML Cite \textit{P. Markowich} et al., J. Funct. Anal. 259, No. 6, 1542--1576 (2010; Zbl 1195.81060) Full Text: DOI arXiv
Béthuel, Fabrice; Danchin, Raphaël; Smets, Didier On the linear wave regime of the Gross-Pitaevskii equation. (English) Zbl 1202.35296 J. Anal. Math. 110, 297-338 (2010). Reviewer: Ma Wen-Xiu (Tampa) MSC: 35Q55 35Q53 37K55 PDF BibTeX XML Cite \textit{F. Béthuel} et al., J. Anal. Math. 110, 297--338 (2010; Zbl 1202.35296) Full Text: DOI
Servadei, Raffaella; Squassina, Marco Soliton dynamics for a general class of Schrödinger equations. (English) Zbl 1186.35208 J. Math. Anal. Appl. 365, No. 2, 776-796 (2010). MSC: 35Q55 35Q51 35C08 35B40 81Q05 PDF BibTeX XML Cite \textit{R. Servadei} and \textit{M. Squassina}, J. Math. Anal. Appl. 365, No. 2, 776--796 (2010; Zbl 1186.35208) Full Text: DOI arXiv
Antoine, Xavier; Besse, Christophe; Klein, Pauline Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. (English) Zbl 1161.65074 J. Comput. Phys. 228, No. 2, 312-335 (2009). MSC: 65M20 65M12 35Q40 81Q05 PDF BibTeX XML Cite \textit{X. Antoine} et al., J. Comput. Phys. 228, No. 2, 312--335 (2009; Zbl 1161.65074) Full Text: DOI