Sacchetti, Andrea Perturbation theory for nonlinear Schrödinger equations. (English) Zbl 1528.35169 Nonlinearity 36, No. 11, 6048-6070 (2023). MSC: 35Q55 81Q15 35B35 PDFBibTeX XMLCite \textit{A. Sacchetti}, Nonlinearity 36, No. 11, 6048--6070 (2023; Zbl 1528.35169) Full Text: DOI arXiv OA License
Carles, Rémi; Il’yasov, Yavdat On ground states for the 2D Schrödinger equation with combined nonlinearities and harmonic potential. (English) Zbl 07778761 Stud. Appl. Math. 150, No. 1, 92-118 (2023). MSC: 35Q55 35Q41 35B35 35A01 35A02 PDFBibTeX XMLCite \textit{R. Carles} and \textit{Y. Il'yasov}, Stud. Appl. Math. 150, No. 1, 92--118 (2023; Zbl 07778761) Full Text: DOI arXiv OA License
Hofstrand, Andrew; Li, Huaiyu; Weinstein, Michael I. Discrete breathers of nonlinear dimer lattices: bridging the anti-continuous and continuous limits. (English) Zbl 1521.34013 J. Nonlinear Sci. 33, No. 4, Paper No. 59, 52 p. (2023). Reviewer: Caidi Zhao (Wenzhou) MSC: 34A33 34C25 34C15 34E10 PDFBibTeX XMLCite \textit{A. Hofstrand} et al., J. Nonlinear Sci. 33, No. 4, Paper No. 59, 52 p. (2023; Zbl 1521.34013) Full Text: DOI arXiv
Masaki, Satoshi; Murphy, Jason; Segata, Jun-Ichi Asymptotic stability of solitary waves for the \(1d\) NLS with an attractive delta potential. (English) Zbl 1516.35384 Discrete Contin. Dyn. Syst. 43, No. 6, 2137-2185 (2023). Reviewer: Rémi Carles (Rennes) MSC: 35Q55 35Q41 35B40 35C08 35P25 PDFBibTeX XMLCite \textit{S. Masaki} et al., Discrete Contin. Dyn. Syst. 43, No. 6, 2137--2185 (2023; Zbl 1516.35384) 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
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
Cuccagna, Scipio; Maeda, Masaya Coordinates at small energy and refined profiles for the nonlinear Schrödinger equation. (English) Zbl 1490.35405 Ann. PDE 7, No. 2, Paper No. 16, 34 p. (2021). MSC: 35Q55 35B35 35B40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, Ann. PDE 7, No. 2, Paper No. 16, 34 p. (2021; Zbl 1490.35405) Full Text: DOI arXiv
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
Maeda, Masaya Stabilization of small solutions of discrete NLS with potential having two eigenvalues. (English) Zbl 1466.35330 Appl. Anal. 100, No. 8, 1603-1633 (2021). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35Q41 35B40 35C08 35B35 81Q05 PDFBibTeX XMLCite \textit{M. Maeda}, Appl. Anal. 100, No. 8, 1603--1633 (2021; Zbl 1466.35330) Full Text: DOI arXiv
Li, Ze Asymptotic stability of solitons to 1D nonlinear Schrödinger equations in subcritical case. (English) Zbl 1465.35360 Front. Math. China 15, No. 5, 923-957 (2020). Reviewer: Jiqiang Zheng (Beijing) MSC: 35Q55 35C08 35B40 35B35 PDFBibTeX XMLCite \textit{Z. Li}, Front. Math. China 15, No. 5, 923--957 (2020; Zbl 1465.35360) Full Text: DOI arXiv
Deng, Qingquan; Yao, Xiaohua Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations with time-dependent potential. (English) Zbl 1443.81029 J. Math. Phys. 61, No. 4, 041504, 35 p. (2020). MSC: 81Q05 81Q10 35Q55 35Q41 35C08 46E39 93B18 PDFBibTeX XMLCite \textit{Q. Deng} and \textit{X. Yao}, J. Math. Phys. 61, No. 4, 041504, 35 p. (2020; Zbl 1443.81029) Full Text: DOI
Masaki, Satoshi; Murphy, Jason; Segata, Jun-ichi Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential. (English) Zbl 1447.35299 Anal. PDE 13, No. 4, 1099-1128 (2020). MSC: 35Q55 35B35 35B40 35C08 35P25 PDFBibTeX XMLCite \textit{S. Masaki} et al., Anal. PDE 13, No. 4, 1099--1128 (2020; Zbl 1447.35299) Full Text: DOI arXiv
Komech, Aleksandr I.; Kopylova, Elena A. Attractors of nonlinear Hamiltonian partial differential equations. (English. Russian original) Zbl 1439.35001 Russ. Math. Surv. 75, No. 1, 1-87 (2020); translation from Usp. Mat. Nauk 75, No. 1, 3-94 (2020). MSC: 35-02 35B41 35B40 35C08 35L71 35B06 PDFBibTeX XMLCite \textit{A. I. Komech} and \textit{E. A. Kopylova}, Russ. Math. Surv. 75, No. 1, 1--87 (2020; Zbl 1439.35001); translation from Usp. Mat. Nauk 75, No. 1, 3--94 (2020) Full Text: DOI arXiv
Naumkin, Ivan; Raphaël, Pierre On traveling waves of the nonlinear Schrödinger equation escaping a potential well. (English) Zbl 1437.35194 Ann. Henri Poincaré 21, No. 5, 1677-1758 (2020). MSC: 35J10 35Q55 PDFBibTeX XMLCite \textit{I. Naumkin} and \textit{P. Raphaël}, Ann. Henri Poincaré 21, No. 5, 1677--1758 (2020; Zbl 1437.35194) Full Text: DOI arXiv
An, Xinliang; Soffer, Avy Fermi’s golden rule and \(H^1\) scattering for nonlinear Klein-Gordon equations with metastable states. (English) Zbl 1431.35145 Discrete Contin. Dyn. Syst. 40, No. 1, 331-373 (2020). MSC: 35Q40 35B34 35B40 35L70 35P25 35C08 PDFBibTeX XMLCite \textit{X. An} and \textit{A. Soffer}, Discrete Contin. Dyn. Syst. 40, No. 1, 331--373 (2020; Zbl 1431.35145) Full Text: DOI arXiv
Comech, Andrew Solutions with compact time spectrum to nonlinear Klein-Gordon and Schrödinger equations and the Titchmarsh theorem for partial convolution. (English) Zbl 1433.37067 Arnold Math. J. 5, No. 2-3, 315-338 (2019). MSC: 37K40 35C05 35Q55 35Q51 PDFBibTeX XMLCite \textit{A. Comech}, Arnold Math. J. 5, No. 2--3, 315--338 (2019; Zbl 1433.37067) Full Text: DOI arXiv
Boussaïd, Nabile; Comech, Andrew Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity. (English) Zbl 1426.35026 J. Funct. Anal. 277, No. 12, Article ID 108289, 68 p. (2019). MSC: 35B35 35Q41 35C08 35P15 PDFBibTeX XMLCite \textit{N. Boussaïd} and \textit{A. Comech}, J. Funct. Anal. 277, No. 12, Article ID 108289, 68 p. (2019; Zbl 1426.35026) Full Text: DOI arXiv
Bourget, Olivier; Courdurier, Matias; Fernández, Claudio Construction of solutions for some localized nonlinear Schrödinger equations. (English) Zbl 1411.35094 Discrete Contin. Dyn. Syst. 39, No. 2, 841-862 (2019). MSC: 35J10 35Q55 PDFBibTeX XMLCite \textit{O. Bourget} et al., Discrete Contin. Dyn. Syst. 39, No. 2, 841--862 (2019; Zbl 1411.35094) Full Text: DOI
Deng, Qingquan; Soffer, Avy; Yao, Xiaohua Soliton-potential interactions for nonlinear Schrödinger equation in \(\mathbb{R}^3\). (English) Zbl 1428.35500 SIAM J. Math. Anal. 50, No. 5, 5243-5292 (2018). MSC: 35Q55 37K40 35B40 35C08 35P25 PDFBibTeX XMLCite \textit{Q. Deng} et al., SIAM J. Math. Anal. 50, No. 5, 5243--5292 (2018; Zbl 1428.35500) Full Text: DOI arXiv
Kirr, E. Long time dynamics and coherent states in nonlinear wave equations. (English) Zbl 1397.35160 Melnik, Roderick (ed.) et al., Recent progress and modern challenges in applied mathematics, modeling and computational science. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-6968-5/hbk; 978-1-4939-6969-2/ebook). Fields Institute Communications 79, 59-88 (2017). Reviewer: Dongbing Zha (Shanghai) MSC: 35L90 35L05 35Q55 35L72 35P25 35-02 35B40 PDFBibTeX XMLCite \textit{E. Kirr}, Fields Inst. Commun. 79, 59--88 (2017; Zbl 1397.35160) Full Text: DOI arXiv
Maeda, Masaya Existence and asymptotic stability of quasi-periodic solutions of discrete NLS with potential. (English) Zbl 1375.35501 SIAM J. Math. Anal. 49, No. 5, 3396-3426 (2017). MSC: 35Q55 35B35 35B40 35B10 PDFBibTeX XMLCite \textit{M. Maeda}, SIAM J. Math. Anal. 49, No. 5, 3396--3426 (2017; Zbl 1375.35501) Full Text: DOI arXiv
Jenkinson, M.; Weinstein, M. I. Discrete solitary waves in systems with nonlocal interactions and the Peierls-Nabarro barrier. (English) Zbl 1397.35276 Commun. Math. Phys. 351, No. 1, 45-94 (2017). Reviewer: Gilles Evéquoz (Delémont) MSC: 35Q55 35C08 35B32 82B20 35R11 35C20 PDFBibTeX XMLCite \textit{M. Jenkinson} and \textit{M. I. Weinstein}, Commun. Math. Phys. 351, No. 1, 45--94 (2017; Zbl 1397.35276) Full Text: DOI arXiv
Soffer, Avy; Zhao, Xiaofei A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS. (English) Zbl 1364.35341 Physica D 320, 77-88 (2016). MSC: 35Q55 35C08 65L15 65M70 PDFBibTeX XMLCite \textit{A. Soffer} and \textit{X. Zhao}, Physica D 320, 77--88 (2016; Zbl 1364.35341) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya On orbital instability of spectrally stable vortices of the NLS in the plane. (English) Zbl 1360.35240 J. Nonlinear Sci. 26, No. 6, 1851-1894 (2016). MSC: 35Q55 35B35 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, J. Nonlinear Sci. 26, No. 6, 1851--1894 (2016; Zbl 1360.35240) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya; Phan, Tuoc V. On small energy stabilization in the NLKG with a trapping potential. (English) Zbl 1356.35142 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 146, 32-58 (2016). Reviewer: Michael Reissig (Freiberg) MSC: 35L71 35L15 PDFBibTeX XMLCite \textit{S. Cuccagna} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 146, 32--58 (2016; Zbl 1356.35142) Full Text: DOI arXiv
Komech, Alexander Attractors of Hamilton nonlinear PDEs. (English) Zbl 1382.35049 Discrete Contin. Dyn. Syst. 36, No. 11, 6201-6256 (2016). Reviewer: Jauber C. Oliveira (Florianopolis) MSC: 35B41 35L70 35Q40 PDFBibTeX XMLCite \textit{A. Komech}, Discrete Contin. Dyn. Syst. 36, No. 11, 6201--6256 (2016; Zbl 1382.35049) Full Text: DOI
Ortoleva, Cecilia; Noja, Diego; Adami, Riccardo Asymptotic stability for standing waves of a NLS equation with subcritical concentrated nonlinearity in dimension three: neutral modes. (English) Zbl 1351.35187 Discrete Contin. Dyn. Syst. 36, No. 11, 5837-5879 (2016). MSC: 35Q55 35Q51 37K40 35B40 35B35 PDFBibTeX XMLCite \textit{C. Ortoleva} et al., Discrete Contin. Dyn. Syst. 36, No. 11, 5837--5879 (2016; Zbl 1351.35187) Full Text: DOI
Sparber, Christof Weakly nonlinear time-adiabatic theory. (English) Zbl 1337.81056 Ann. Henri Poincaré 17, No. 4, 913-936 (2016). Reviewer: Ma Wen-Xiu (Tampa) MSC: 81Q05 35Q41 35Q55 70H11 PDFBibTeX XMLCite \textit{C. Sparber}, Ann. Henri Poincaré 17, No. 4, 913--936 (2016; Zbl 1337.81056) Full Text: DOI arXiv
Cuccagna, Scipio; Tarulli, Mirko On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential. (English) Zbl 1334.35264 J. Math. Anal. Appl. 436, No. 2, 1332-1368 (2016). MSC: 35Q41 35B32 35Q55 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Tarulli}, J. Math. Anal. Appl. 436, No. 2, 1332--1368 (2016; Zbl 1334.35264) Full Text: DOI arXiv
Jenkinson, M.; Weinstein, M. I. Onsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls-Nabarro barrier. (English) Zbl 1357.37087 Nonlinearity 29, No. 1, 27-86 (2016). MSC: 37L60 39A22 35Q55 39A14 PDFBibTeX XMLCite \textit{M. Jenkinson} and \textit{M. I. Weinstein}, Nonlinearity 29, No. 1, 27--86 (2016; Zbl 1357.37087) Full Text: DOI arXiv
Derks, Gianne Stability of fronts in inhomogeneous wave equations. (English) Zbl 1320.35134 Acta Appl. Math. 137, No. 1, 61-78 (2015). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35C07 35B35 35Q53 35Q41 37K45 35L71 PDFBibTeX XMLCite \textit{G. Derks}, Acta Appl. Math. 137, No. 1, 61--78 (2015; Zbl 1320.35134) Full Text: DOI Link
Dejak, S. I.; Egli, D.; Lushnikov, P. M.; Sigal, I. M. On blowup dynamics in the Keller-Segel model of chemotaxis. (English) Zbl 1326.35049 St. Petersbg. Math. J. 25, No. 4, 547-574 (2014) and Algebra Anal. 25, No. 4, 47-84 (2013). MSC: 35B44 35K51 35K57 35Q84 92C17 PDFBibTeX XMLCite \textit{S. I. Dejak} et al., St. Petersbg. Math. J. 25, No. 4, 547--574 (2014; Zbl 1326.35049) Full Text: DOI arXiv
Komech, A.; Kopylova, E. On eigenfunction expansion of solutions to the Hamilton equations. (English) Zbl 1300.34195 J. Stat. Phys. 154, No. 1-2, 503-521 (2014). Reviewer: Zaki El Mehi (Alexandria) MSC: 34L10 83A05 34A30 PDFBibTeX XMLCite \textit{A. Komech} and \textit{E. Kopylova}, J. Stat. Phys. 154, No. 1--2, 503--521 (2014; Zbl 1300.34195) 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
Komech, Alexander I.; Kopylova, Elena A.; Kopylov, Sergey A. On nonlinear wave equations with parabolic potentials. (English) Zbl 1295.35063 J. Spectr. Theory 3, No. 4, 485-503 (2013). MSC: 35B35 37K40 35L71 35C08 35Q56 PDFBibTeX XMLCite \textit{A. I. Komech} et al., J. Spectr. Theory 3, No. 4, 485--503 (2013; Zbl 1295.35063) Full Text: DOI arXiv
Imaykin, V. M. Soliton asymptotics for systems of ‘field-particle’ type. (English. Russian original) Zbl 1307.35288 Russ. Math. Surv. 68, No. 2, 227-281 (2013); translation from Usp. Mat. Nauk. 68, No. 2, 33-90 (2013). MSC: 35Q60 35Q61 78A35 81U99 37K40 PDFBibTeX XMLCite \textit{V. M. Imaykin}, Russ. Math. Surv. 68, No. 2, 227--281 (2013; Zbl 1307.35288); translation from Usp. Mat. Nauk. 68, No. 2, 33--90 (2013) Full Text: DOI
Pelinovsky, Dmitry E.; Stefanov, Atanas Asymptotic stability of small gap solitons in nonlinear Dirac equations. (English) Zbl 1279.35083 J. Math. Phys. 53, No. 7, 073705, 27 p. (2012). Reviewer: Dian K. Palagachev (Bari) MSC: 35Q55 35C08 35C07 35B35 PDFBibTeX XMLCite \textit{D. E. Pelinovsky} and \textit{A. Stefanov}, J. Math. Phys. 53, No. 7, 073705, 27 p. (2012; Zbl 1279.35083) Full Text: DOI arXiv
Nakanishi, Kenji; Van Phan, Tuoc; Tsai, Tai-Peng Small solutions of nonlinear Schrödinger equations near first excited states. (English) Zbl 1244.35136 J. Funct. Anal. 263, No. 3, 703-781 (2012). MSC: 35Q55 81Q05 35P05 PDFBibTeX XMLCite \textit{K. Nakanishi} et al., J. Funct. Anal. 263, No. 3, 703--781 (2012; Zbl 1244.35136) 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
Kopylova, E.; Komech, A. I. On asymptotic stability of kink for relativistic Ginzburg-Landau equations. (English) Zbl 1256.35146 Arch. Ration. Mech. Anal. 202, No. 1, 213-245 (2011). MSC: 35Q56 35Q75 83A05 PDFBibTeX XMLCite \textit{E. Kopylova} and \textit{A. I. Komech}, Arch. Ration. Mech. Anal. 202, No. 1, 213--245 (2011; Zbl 1256.35146) Full Text: DOI arXiv
Cuccagna, Scipio The Hamiltonian structure of the nonlinear Schrödinger equation and the asymptotic stability of its ground states. (English) Zbl 1222.35183 Commun. Math. Phys. 305, No. 2, 279-331 (2011). MSC: 35Q55 35B40 35B35 PDFBibTeX XMLCite \textit{S. Cuccagna}, Commun. Math. Phys. 305, No. 2, 279--331 (2011; Zbl 1222.35183) Full Text: DOI arXiv
Komech, A. I.; Kopylova, E. A.; Spohn, H. Scattering of solitons for Dirac equation coupled to a particle. (English) Zbl 1229.35228 J. Math. Anal. Appl. 383, No. 2, 265-290 (2011). Reviewer: M. Marin (Brasov) MSC: 35Q51 35C08 34L40 37J10 37M15 PDFBibTeX XMLCite \textit{A. I. Komech} et al., J. Math. Anal. Appl. 383, No. 2, 265--290 (2011; Zbl 1229.35228) Full Text: DOI arXiv
Cuccagna, Scipio; Visciglia, Nicola On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D. (English) Zbl 1298.35191 Trans. Am. Math. Soc. 363, No. 5, 2357-2391 (2011). Reviewer: Marcelo M. Cavalcanti (Maringá) MSC: 35Q55 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{N. Visciglia}, Trans. Am. Math. Soc. 363, No. 5, 2357--2391 (2011; Zbl 1298.35191) Full Text: DOI arXiv
Koo, Eva Asymptotic stability of small solitary waves for nonlinear Schrödinger equations with electromagnetic potential in \(\mathbb R^3\). (English) Zbl 1211.35252 J. Differ. Equations 250, No. 8, 3473-3503 (2011). MSC: 35Q55 35B40 35B35 35C08 78A25 35B45 PDFBibTeX XMLCite \textit{E. Koo}, J. Differ. Equations 250, No. 8, 3473--3503 (2011; Zbl 1211.35252) Full Text: DOI arXiv
Goldberg, Michael A dispersive bound for three-dimensional Schrödinger operators with zero energy eigenvalues. (English) Zbl 1223.35265 Commun. Partial Differ. Equations 35, No. 9, 1610-1634 (2010). Reviewer: Nils Ackermann (Mexico City) MSC: 35Q41 81U30 35J10 47D08 PDFBibTeX XMLCite \textit{M. Goldberg}, Commun. Partial Differ. Equations 35, No. 9, 1610--1634 (2010; Zbl 1223.35265) Full Text: DOI arXiv
Kopylova, E. A. On asymptotic stability of solitary waves in discrete Klein-Gordon equation coupled to a nonlinear oscillator. (English) Zbl 1207.39021 Appl. Anal. 89, No. 9, 1467-1492 (2010). Reviewer: Fei Xue (Hartford) MSC: 39A30 39A14 39A12 35Q40 81Q05 37K10 PDFBibTeX XMLCite \textit{E. A. Kopylova}, Appl. Anal. 89, No. 9, 1467--1492 (2010; Zbl 1207.39021) Full Text: DOI
Kirr, E.; Mızrak, Ö. Asymptotic stability of ground states in 3D nonlinear Schrödinger equation including subcritical cases. (English) Zbl 1187.35238 J. Funct. Anal. 257, No. 12, 3691-3747 (2009). Reviewer: Hideo Yamagata (Osaka) MSC: 35Q55 81Q10 35B35 35B40 PDFBibTeX XMLCite \textit{E. Kirr} and \textit{Ö. Mızrak}, J. Funct. Anal. 257, No. 12, 3691--3747 (2009; Zbl 1187.35238) 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
Cuccagna, Scipio; Tarulli, Mirko On asymptotic stability in energy space of ground states of NLS in 2D. (English) Zbl 1171.35470 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 4, 1361-1386 (2009). MSC: 35Q55 35B35 35B40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Tarulli}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 4, 1361--1386 (2009; Zbl 1171.35470) Full Text: DOI arXiv EuDML
Kopylova, E. A. On the asymptotic stability of solitary waves in the discrete Schrödinger equation coupled to a nonlinear oscillator. (English) Zbl 1167.35515 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7-8, 3031-3046 (2009). MSC: 35Q55 37K40 39A12 PDFBibTeX XMLCite \textit{E. A. Kopylova}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7--8, 3031--3046 (2009; Zbl 1167.35515) Full Text: DOI
Kirr, E.; Zarnescu, A. Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases. (English) Zbl 1171.35112 J. Differ. Equations 247, No. 3, 710-735 (2009). MSC: 35Q55 35B40 35B35 35B45 PDFBibTeX XMLCite \textit{E. Kirr} and \textit{A. Zarnescu}, J. Differ. Equations 247, No. 3, 710--735 (2009; Zbl 1171.35112) Full Text: DOI arXiv
Cuccagna, Scipio On instability of excited states of the nonlinear Schrödinger equation. (English) Zbl 1161.35500 Physica D 238, No. 1, 38-54 (2009). MSC: 35Q55 35B35 37K45 PDFBibTeX XMLCite \textit{S. Cuccagna}, Physica D 238, No. 1, 38--54 (2009; Zbl 1161.35500) Full Text: DOI arXiv
Goodman, Roy H.; Weinstein, Michael I. Stability and instability of nonlinear defect states in the coupled mode equations-analytical and numerical study. (English) Zbl 1153.78325 Physica D 237, No. 21, 2731-2760 (2008). MSC: 78A60 35Q55 78A40 PDFBibTeX XMLCite \textit{R. H. Goodman} and \textit{M. I. Weinstein}, Physica D 237, No. 21, 2731--2760 (2008; Zbl 1153.78325) Full Text: DOI arXiv
Cuccagna, Scipio; Mizumachi, Tetsu On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations. (English) Zbl 1155.35092 Commun. Math. Phys. 284, No. 1, 51-77 (2008). MSC: 35Q55 35B35 35B40 81Q05 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{T. Mizumachi}, Commun. Math. Phys. 284, No. 1, 51--77 (2008; Zbl 1155.35092) Full Text: DOI arXiv
Buslaev, V. S.; Komech, A. I.; Kopylova, E. A.; Stuart, D. On asymptotic stability of solitary waves in Schrödinger equation coupled to nonlinear oscillator. (English) Zbl 1185.35247 Commun. Partial Differ. Equations 33, No. 4, 669-705 (2008). Reviewer: Igor Andrianov (Köln) MSC: 35Q55 35Q51 35B35 35B40 37K40 PDFBibTeX XMLCite \textit{V. S. Buslaev} et al., Commun. Partial Differ. Equations 33, No. 4, 669--705 (2008; Zbl 1185.35247) Full Text: DOI arXiv
Cuccagna, Scipio On asymptotic stability in energy space of ground states of NLS in 1D. (English) Zbl 1185.35251 J. Differ. Equations 245, No. 3, 653-691 (2008). Reviewer: Igor Andrianov (Köln) MSC: 35Q55 35B35 35B40 PDFBibTeX XMLCite \textit{S. Cuccagna}, J. Differ. Equations 245, No. 3, 653--691 (2008; Zbl 1185.35251) Full Text: DOI arXiv Numdam
Zhou, Gang Perturbation expansion and \(N\)th order Fermi golden rule of the nonlinear Schrödinger equations. (English) Zbl 1144.81430 J. Math. Phys. 48, No. 5, 053509, 23 p. (2007). MSC: 47N50 35Q55 81Q15 PDFBibTeX XMLCite \textit{G. Zhou}, J. Math. Phys. 48, No. 5, 053509, 23 p. (2007; Zbl 1144.81430) Full Text: DOI
Gang, Zhou; Sigal, I. M. Relaxation of solitons in nonlinear Schrödinger equations with potential. (English) Zbl 1126.35065 Adv. Math. 216, No. 2, 443-490 (2007). MSC: 35Q55 37K45 81R12 PDFBibTeX XMLCite \textit{Z. Gang} and \textit{I. M. Sigal}, Adv. Math. 216, No. 2, 443--490 (2007; Zbl 1126.35065) Full Text: DOI arXiv
Boussaid, Nabile Stable directions for small nonlinear Dirac standing waves. (English) Zbl 1127.35060 Commun. Math. Phys. 268, No. 3, 757-817 (2006). MSC: 35Q55 37K45 81Q05 35P25 PDFBibTeX XMLCite \textit{N. Boussaid}, Commun. Math. Phys. 268, No. 3, 757--817 (2006; Zbl 1127.35060) Full Text: DOI arXiv
Imaikin, Valery; Komech, Alexander; Vainberg, Boris On scattering of solitons for the Klein-Gordon equation coupled to a particle. (English) Zbl 1127.35054 Commun. Math. Phys. 268, No. 2, 321-367 (2006). MSC: 35Q40 81U05 37K40 35P25 35Q51 35L70 PDFBibTeX XMLCite \textit{V. Imaikin} et al., Commun. Math. Phys. 268, No. 2, 321--367 (2006; Zbl 1127.35054) Full Text: DOI arXiv
Komech, A.; Kopylova, E. Scattering of solitons for the Schrödinger equation coupled to a particle. (English) Zbl 1118.35040 Russ. J. Math. Phys. 13, No. 2, 158-187 (2006). Reviewer: Wuquing Ning (Tokyo) MSC: 35Q40 81Q05 81U15 35Q51 37K40 PDFBibTeX XMLCite \textit{A. Komech} and \textit{E. Kopylova}, Russ. J. Math. Phys. 13, No. 2, 158--187 (2006; Zbl 1118.35040) Full Text: DOI arXiv
Cuccagna, Scipio Stability of standing waves for NLS with perturbed Lamé potential. (English) Zbl 1115.35120 J. Differ. Equations 223, No. 1, 112-160 (2006). Reviewer: Ma Wen-Xiu (Tampa) MSC: 35Q55 37K45 37K15 PDFBibTeX XMLCite \textit{S. Cuccagna}, J. Differ. Equations 223, No. 1, 112--160 (2006; Zbl 1115.35120) Full Text: DOI
Cuccagna, S.; Kirr, E.; Pelinovsky, D. Parametric resonance of ground states in the nonlinear Schrödinger equation. (English) Zbl 1081.35101 J. Differ. Equations 220, No. 1, 85-120 (2006). MSC: 35Q55 35B40 81Q10 PDFBibTeX XMLCite \textit{S. Cuccagna} et al., J. Differ. Equations 220, No. 1, 85--120 (2006; Zbl 1081.35101) Full Text: DOI
Fröhlich, J.; Gustafson, S.; Jonsson, B. L. G.; Sigal, I. M. Solitary wave dynamics in an external potential. (English) Zbl 1075.35075 Commun. Math. Phys. 250, No. 3, 613-642 (2004). MSC: 35Q55 35Q51 37K25 37K40 PDFBibTeX XMLCite \textit{J. Fröhlich} et al., Commun. Math. Phys. 250, No. 3, 613--642 (2004; Zbl 1075.35075) Full Text: DOI arXiv
Tsai, Tai-Peng Asymptotic dynamics of nonlinear Schrödinger equations with many bound states. (English) Zbl 1038.35128 J. Differ. Equations 192, No. 1, 225-282 (2003). Reviewer: Andrew Pickering (Salamanca) MSC: 35Q55 35Q40 81Q05 PDFBibTeX XMLCite \textit{T.-P. Tsai}, J. Differ. Equations 192, No. 1, 225--282 (2003; Zbl 1038.35128) Full Text: DOI arXiv