Ling, Liming; Sun, Xuan Stability of elliptic function solutions for the focusing modified KdV equation. (English) Zbl 07797718 Adv. Math. 435, Part A, Article ID 109356, 63 p. (2023). MSC: 35Q53 37K35 35B20 35B35 35B40 35C08 33E05 PDFBibTeX XMLCite \textit{L. Ling} and \textit{X. Sun}, Adv. Math. 435, Part A, Article ID 109356, 63 p. (2023; Zbl 07797718) Full Text: DOI arXiv
Hannani, Amirali; Olla, Stefano A stochastic thermalization of the discrete nonlinear Schrödinger equation. (English) Zbl 07772833 Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 4, 1379-1415 (2023). Reviewer: Chenjie Fan (Beijing) MSC: 35Q55 35Q41 39A12 60F10 35C08 35H10 35B20 35R60 PDFBibTeX XMLCite \textit{A. Hannani} and \textit{S. Olla}, Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 4, 1379--1415 (2023; Zbl 07772833) Full Text: DOI arXiv
Sun, Wen-Rong Spectral stability of elliptic solutions to the short-pulse equation. (English) Zbl 1527.35124 Physica D 456, Article ID 133916, 6 p. (2023). MSC: 35C07 35B35 35Q55 PDFBibTeX XMLCite \textit{W.-R. Sun}, Physica D 456, Article ID 133916, 6 p. (2023; Zbl 1527.35124) Full Text: DOI
Aiki, Masashi The Hasimoto transformation for a finite length vortex filament and its application. (English) Zbl 1527.35255 SIAM J. Math. Anal. 55, No. 6, 7273-7295 (2023). MSC: 35Q35 35Q55 35B35 PDFBibTeX XMLCite \textit{M. Aiki}, SIAM J. Math. Anal. 55, No. 6, 7273--7295 (2023; Zbl 1527.35255) Full Text: DOI arXiv
Cox, Graham; Curran, Mitchell; Latushkin, Yuri; Marangell, Robert Hamiltonian spectral flows, the Maslov index, and the stability of standing waves in the nonlinear Schrödinger equation. (English) Zbl 1526.34064 SIAM J. Math. Anal. 55, No. 5, 4998-5050 (2023). Reviewer: Rakib Efendiev (Baku) MSC: 34L05 34L15 34L40 37K25 34C37 47E05 53D12 PDFBibTeX XMLCite \textit{G. Cox} et al., SIAM J. Math. Anal. 55, No. 5, 4998--5050 (2023; Zbl 1526.34064) Full Text: DOI arXiv
Hong, Si-Yu; Zhang, Wei-Guo; Ling, Xing-Qian Orbital stability of dn periodic wave solutions of the Boussinesq equation with quadratic-cubic nonlinear terms. (English) Zbl 1519.35024 J. Nonlinear Math. Phys. 30, No. 2, 455-474 (2023). MSC: 35B35 35Q51 35C07 37K45 PDFBibTeX XMLCite \textit{S.-Y. Hong} et al., J. Nonlinear Math. Phys. 30, No. 2, 455--474 (2023; Zbl 1519.35024) Full Text: DOI
Sun, Wen-Rong The orbital stability of the periodic traveling wave solutions to the defocusing complex modified Korteweg-de Vries equation. (English) Zbl 1509.37104 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 227, Article ID 113155, 21 p. (2023). MSC: 37K45 35Q53 35C07 35C08 PDFBibTeX XMLCite \textit{W.-R. Sun}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 227, Article ID 113155, 21 p. (2023; Zbl 1509.37104) Full Text: DOI arXiv
Alves, Giovana; Natali, Fábio Periodic waves for the cubic-quintic nonlinear Schrödinger equation: existence and orbital stability. (English) Zbl 1501.35359 Discrete Contin. Dyn. Syst., Ser. B 28, No. 2, 854-871 (2023). MSC: 35Q55 35Q41 37K45 37K40 35A01 35B35 35B10 33E05 PDFBibTeX XMLCite \textit{G. Alves} and \textit{F. Natali}, Discrete Contin. Dyn. Syst., Ser. B 28, No. 2, 854--871 (2023; Zbl 1501.35359) Full Text: DOI arXiv
Bittencourt Moraes, Gabriel E.; Borluk, Handan; de Loreno, Guilherme; Muslu, Gulcin M.; Natali, Fábio Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation. (English) Zbl 1512.35608 J. Differ. Equations 341, 263-291 (2022). MSC: 35R11 35B35 35C07 35Q55 PDFBibTeX XMLCite \textit{G. E. Bittencourt Moraes} et al., J. Differ. Equations 341, 263--291 (2022; Zbl 1512.35608) Full Text: DOI arXiv
Chauleur, Quentin; Faou, Erwan Around plane waves solutions of the Schrödinger-Langevin equation. (English) Zbl 1497.35401 SIAM J. Math. Anal. 54, No. 5, 5103-5125 (2022). MSC: 35Q40 35Q55 35Q41 35B40 35B65 82C31 35R60 65T50 PDFBibTeX XMLCite \textit{Q. Chauleur} and \textit{E. Faou}, SIAM J. Math. Anal. 54, No. 5, 5103--5125 (2022; Zbl 1497.35401) Full Text: DOI arXiv
Hakkaev, Sevdzhan; Stanislavova, Milena; Stefanov, Atanas On the stability of the periodic waves for the Benney system. (English) Zbl 1492.35308 SIAM J. Appl. Dyn. Syst. 21, No. 3, 1726-1747 (2022). MSC: 35Q55 35B35 35B40 35G30 PDFBibTeX XMLCite \textit{S. Hakkaev} et al., SIAM J. Appl. Dyn. Syst. 21, No. 3, 1726--1747 (2022; Zbl 1492.35308) Full Text: DOI arXiv
Jaquette, Jonathan; Lessard, Jean-Philippe; Takayasu, Akitoshi Global dynamics in nonconservative nonlinear Schrödinger equations. (English) Zbl 1492.35309 Adv. Math. 398, Article ID 108234, 70 p. (2022). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35B40 35B20 37K99 37M21 35A01 PDFBibTeX XMLCite \textit{J. Jaquette} et al., Adv. Math. 398, Article ID 108234, 70 p. (2022; Zbl 1492.35309) Full Text: DOI arXiv
Gaebler, Harrison; Stanislavova, Milena NLS and KdV Hamiltonian linearized operators: a priori bounds on the spectrum and optimal \(L^2\) estimates for the semigroups. (English) Zbl 07493963 Physica D 416, Article ID 132738, 13 p. (2021). MSC: 47N20 35Q53 35Q55 PDFBibTeX XMLCite \textit{H. Gaebler} and \textit{M. Stanislavova}, Physica D 416, Article ID 132738, 13 p. (2021; Zbl 07493963) Full Text: DOI
Leisman, Katelyn Plaisier; Bronski, Jared C.; Johnson, Mathew A.; Marangell, Robert Stability of traveling wave solutions of nonlinear dispersive equations of NLS type. (English) Zbl 1467.35299 Arch. Ration. Mech. Anal. 240, No. 2, 927-969 (2021). MSC: 35Q55 35C07 35B10 35B20 65N25 PDFBibTeX XMLCite \textit{K. P. Leisman} et al., Arch. Ration. Mech. Anal. 240, No. 2, 927--969 (2021; Zbl 1467.35299) Full Text: DOI arXiv
Sacchetti, Andrea Stationary solutions to cubic nonlinear Schrödinger equations with quasi-periodic boundary conditions. (English) Zbl 1519.35304 J. Phys. A, Math. Theor. 53, No. 38, Article ID 385204, 16 p. (2020). MSC: 35Q55 81S08 PDFBibTeX XMLCite \textit{A. Sacchetti}, J. Phys. A, Math. Theor. 53, No. 38, Article ID 385204, 16 p. (2020; Zbl 1519.35304) Full Text: DOI arXiv
Deconinck, Bernard; Upsal, Jeremy The orbital stability of elliptic solutions of the focusing nonlinear Schrödinger equation. (English) Zbl 1437.37096 SIAM J. Math. Anal. 52, No. 1, 1-41 (2020). Reviewer: Anthony D. Osborne (Keele) MSC: 37K45 37K55 35Q55 PDFBibTeX XMLCite \textit{B. Deconinck} and \textit{J. Upsal}, SIAM J. Math. Anal. 52, No. 1, 1--41 (2020; Zbl 1437.37096) Full Text: DOI arXiv
Hayashi, Masayuki Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation. (English) Zbl 1420.35356 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 36, No. 5, 1331-1360 (2019). MSC: 35Q55 35C07 33E05 35C08 PDFBibTeX XMLCite \textit{M. Hayashi}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 36, No. 5, 1331--1360 (2019; Zbl 1420.35356) Full Text: DOI arXiv
Claassen, Kyle M.; Johnson, Mathew A. Nondegeneracy and stability of antiperiodic bound states for fractional nonlinear Schrödinger equations. (English) Zbl 1417.35176 J. Differ. Equations 266, No. 9, 5664-5712 (2019). Reviewer: Alessandro Selvitella (Fort Wayne) MSC: 35Q55 35R11 35B35 35P30 PDFBibTeX XMLCite \textit{K. M. Claassen} and \textit{M. A. Johnson}, J. Differ. Equations 266, No. 9, 5664--5712 (2019; Zbl 1417.35176) Full Text: DOI arXiv
Maspero, A.; Procesi, M. Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation on \(\mathbb{T}^2\). (English) Zbl 1428.35529 J. Differ. Equations 265, No. 7, 3212-3309 (2018). MSC: 35Q55 35B35 PDFBibTeX XMLCite \textit{A. Maspero} and \textit{M. Procesi}, J. Differ. Equations 265, No. 7, 3212--3309 (2018; Zbl 1428.35529) Full Text: DOI arXiv
Deconinck, Bernard; Segal, Benjamin L. The stability spectrum for elliptic solutions to the focusing NLS equation. (English) Zbl 1415.35251 Physica D 346, 1-19 (2017). MSC: 35Q55 35B35 35P15 35B10 PDFBibTeX XMLCite \textit{B. Deconinck} and \textit{B. L. Segal}, Physica D 346, 1--19 (2017; Zbl 1415.35251) Full Text: DOI arXiv
Pava, Jaime Angulo; Plaza, Ramón G. Transverse orbital stability of periodic traveling waves for nonlinear Klein-Gordon equations. (English) Zbl 1360.35229 Stud. Appl. Math. 137, No. 4, 473-501 (2016). Reviewer: Aleksey Kostenko (Donetsk) MSC: 35Q53 35C07 35B35 35B10 PDFBibTeX XMLCite \textit{J. A. Pava} and \textit{R. G. Plaza}, Stud. Appl. Math. 137, No. 4, 473--501 (2016; Zbl 1360.35229) Full Text: DOI
Johnson, Edward R.; Pelinovsky, Dmitry E. Orbital stability of periodic waves in the class of reduced Ostrovsky equations. (English) Zbl 1355.35017 J. Differ. Equations 261, No. 6, 3268-3304 (2016). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35B35 37K10 PDFBibTeX XMLCite \textit{E. R. Johnson} and \textit{D. E. Pelinovsky}, J. Differ. Equations 261, No. 6, 3268--3304 (2016; Zbl 1355.35017) Full Text: DOI arXiv
Innocenti, Giacomo; Paoletti, Paolo Embedding dynamical networks into distributed models. (English) Zbl 1463.35077 Commun. Nonlinear Sci. Numer. Simul. 24, No. 1-3, 21-39 (2015). MSC: 35B35 93A14 93C20 35G20 PDFBibTeX XMLCite \textit{G. Innocenti} and \textit{P. Paoletti}, Commun. Nonlinear Sci. Numer. Simul. 24, No. 1--3, 21--39 (2015; Zbl 1463.35077) Full Text: DOI
Demirkaya, Aslihan; Hakkaev, Sevdzhan On the spectral stability of periodic waves of the coupled Schrödinger equations. (English) Zbl 1349.35349 Phys. Lett., A 379, No. 45-46, 2908-2914 (2015). MSC: 35Q55 35B35 35P99 PDFBibTeX XMLCite \textit{A. Demirkaya} and \textit{S. Hakkaev}, Phys. Lett., A 379, No. 45--46, 2908--2914 (2015; Zbl 1349.35349) Full Text: DOI
De Bièvre, Stephan; Genoud, François; Nodari, Simona Rota Orbital stability: analysis meets geometry. (English) Zbl 1347.37122 Besse, Christophe (ed.) et al., Nonlinear optical and atomic systems. At the interface of physics and mathematics. Based on lecture notes given at the 2013 Painlevé-CEMPI-PhLAM thematic semester. Cham: Springer; Lille: Centre Européen pour les Mathématiques, la Physiques et leurs Interactions (CEMPI) (ISBN 978-3-319-19014-3/pbk; 978-3-319-19015-0/ebook). Lecture Notes in Mathematics 2146, 147-273 (2015). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37K45 37K05 37J25 37-01 35Q55 PDFBibTeX XMLCite \textit{S. De Bièvre} et al., Lect. Notes Math. 2146, 147--273 (2015; Zbl 1347.37122) Full Text: DOI arXiv
Kapitula, Todd; Deconinck, Bernard On the spectral and orbital stability of spatially periodic stationary solutions of generalized Korteweg-de Vries equations. (English) Zbl 1331.35305 Guyenne, Philippe (ed.) et al., Hamiltonian partial differential equations and applications. Selected papers based on the presentations at the conference on Hamiltonian PDEs: analysis, computations and applications, Toronto, Canada, January 10–12, 2014. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-2949-8/hbk; 978-1-4939-2950-4/ebook). Fields Institute Communications 75, 285-322 (2015). MSC: 35Q53 PDFBibTeX XMLCite \textit{T. Kapitula} and \textit{B. Deconinck}, Fields Inst. Commun. 75, 285--322 (2015; Zbl 1331.35305) Full Text: DOI
Wilson, Bobby Sobolev stability of plane wave solutions to the nonlinear Schrödinger equation. (English) Zbl 1328.35222 Commun. Partial Differ. Equations 40, No. 8, 1521-1542 (2015). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q55 PDFBibTeX XMLCite \textit{B. Wilson}, Commun. Partial Differ. Equations 40, No. 8, 1521--1542 (2015; Zbl 1328.35222) Full Text: DOI arXiv
Gallay, Thierry; Pelinovsky, Dmitry Orbital stability in the cubic defocusing NLS equation. I: Cnoidal periodic waves. (English) Zbl 1326.35340 J. Differ. Equations 258, No. 10, 3607-3638 (2015). Reviewer: Alessandro Selvitella (Hamilton) MSC: 35Q55 35B10 35B35 PDFBibTeX XMLCite \textit{T. Gallay} and \textit{D. Pelinovsky}, J. Differ. Equations 258, No. 10, 3607--3638 (2015; Zbl 1326.35340) Full Text: DOI arXiv
Jones, Christopher K. R. T.; Marangell, Robert; Miller, Peter D.; Plaza, Ramón G. Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation. (English) Zbl 1304.35079 J. Differ. Equations 257, No. 12, 4632-4703 (2014). MSC: 35B35 37J25 70H12 35L71 35B10 PDFBibTeX XMLCite \textit{C. K. R. T. Jones} et al., J. Differ. Equations 257, No. 12, 4632--4703 (2014; Zbl 1304.35079) Full Text: DOI arXiv
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd An instability index theory for quadratic pencils and applications. (English) Zbl 1301.35081 Commun. Math. Phys. 327, No. 2, 521-550 (2014). Reviewer: Miloš Čanak (Beograd) MSC: 35P99 35C07 35Q53 PDFBibTeX XMLCite \textit{J. Bronski} et al., Commun. Math. Phys. 327, No. 2, 521--550 (2014; Zbl 1301.35081) Full Text: DOI arXiv
Jones, Christopher K. R. T.; Marangell, Robert; Miller, Peter D.; Plaza, Ramón G. On the stability analysis of periodic sine-Gordon traveling waves. (English) Zbl 1278.35046 Physica D 251, 63-74 (2013). MSC: 35C07 81Q05 35B35 PDFBibTeX XMLCite \textit{C. K. R. T. Jones} et al., Physica D 251, 63--74 (2013; Zbl 1278.35046) Full Text: DOI arXiv
Pava, Jaime Angulo; Ponce, Gustavo The non-linear Schrödinger equation with a periodic \(\delta\)-interaction. (English) Zbl 1274.76175 Bull. Braz. Math. Soc. (N.S.) 44, No. 3, 497-551 (2013). MSC: 76B25 35Q51 35Q53 PDFBibTeX XMLCite \textit{J. A. Pava} and \textit{G. Ponce}, Bull. Braz. Math. Soc. (N.S.) 44, No. 3, 497--551 (2013; Zbl 1274.76175) Full Text: DOI arXiv
Faou, Erwan; Gauckler, Ludwig; Lubich, Christian Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus. (English) Zbl 1274.35357 Commun. Partial Differ. Equations 38, No. 7-9, 1123-1140 (2013). MSC: 35Q55 37K55 35B20 35B35 PDFBibTeX XMLCite \textit{E. Faou} et al., Commun. Partial Differ. Equations 38, No. 7--9, 1123--1140 (2013; Zbl 1274.35357) Full Text: DOI arXiv
Angulo Pava, Jaime Instability of cnoidal-peak for the NLS-\(\delta\) equation. (English) Zbl 1326.81059 Math. Nachr. 285, No. 13, 1572-1602 (2012). MSC: 81Q05 35Q55 PDFBibTeX XMLCite \textit{J. Angulo Pava}, Math. Nachr. 285, No. 13, 1572--1602 (2012; Zbl 1326.81059) Full Text: DOI
Banquet Brango, Carlos The symmetric regularized-long-wave equation: well-posedness and nonlinear stability. (English) Zbl 1252.35130 Physica D 241, No. 2, 125-133 (2012). MSC: 35G25 35C07 35B35 PDFBibTeX XMLCite \textit{C. Banquet Brango}, Physica D 241, No. 2, 125--133 (2012; Zbl 1252.35130) Full Text: DOI arXiv
Angulo, Jaime; Scialom, Márcia; Banquet, Carlos The regularized Benjamin-Ono and BBM equations: well-posedness and nonlinear stability. (English) Zbl 1210.35205 J. Differ. Equations 250, No. 11, 4011-4036 (2011). MSC: 35Q53 35B35 35B10 PDFBibTeX XMLCite \textit{J. Angulo} et al., J. Differ. Equations 250, No. 11, 4011--4036 (2011; Zbl 1210.35205) Full Text: DOI
Neves, Aloisio Erratum to: Floquet’s theorem and stability of periodic solitary waves. (English) Zbl 1235.34227 J. Dyn. Differ. Equations 22, No. 3, 617-627 (2010). Reviewer: Chie-Ping Chu (Taipei) MSC: 34L15 34L05 34L40 PDFBibTeX XMLCite \textit{A. Neves}, J. Dyn. Differ. Equations 22, No. 3, 617--627 (2010; Zbl 1235.34227) Full Text: DOI
Bronski, Jared C.; Johnson, Mathew A. The modulational instability for a generalized Korteweg-de Vries equation. (English) Zbl 1221.35325 Arch. Ration. Mech. Anal. 197, No. 2, 357-400 (2010). MSC: 35Q53 35B35 PDFBibTeX XMLCite \textit{J. C. Bronski} and \textit{M. A. Johnson}, Arch. Ration. Mech. Anal. 197, No. 2, 357--400 (2010; Zbl 1221.35325) Full Text: DOI arXiv
Deconinck, Bernard; Lovit, David O. Data analysis and reduction using stationary solutions of the NLS equation. (English) Zbl 1191.81110 Appl. Anal. 89, No. 4, 611-626 (2010). MSC: 81Q05 35Q55 37K10 42A65 PDFBibTeX XMLCite \textit{B. Deconinck} and \textit{D. O. Lovit}, Appl. Anal. 89, No. 4, 611--626 (2010; Zbl 1191.81110) Full Text: DOI
Neves, Aloisio Floquet’s theorem and stability of periodic solitary waves. (English) Zbl 1235.34226 J. Dyn. Differ. Equations 21, No. 3, 555-565 (2009); erratum 22, No. 3, 617-627 (2010). MSC: 34L15 34L05 34L40 PDFBibTeX XMLCite \textit{A. Neves}, J. Dyn. Differ. Equations 21, No. 3, 555--565 (2009; Zbl 1235.34226) Full Text: DOI
Hařaǧuş, Mariana; Kapitula, Todd On the spectra of periodic waves for infinite-dimensional Hamiltonian systems. (English) Zbl 1155.37039 Physica D 237, No. 20, 2649-2671 (2008). Reviewer: Vjacheslav Yurko (Saratov) MSC: 37K15 35Q53 35Q55 35B10 PDFBibTeX XMLCite \textit{M. Hařaǧuş} and \textit{T. Kapitula}, Physica D 237, No. 20, 2649--2671 (2008; Zbl 1155.37039) Full Text: DOI
Ivey, T.; Lafortune, S. Spectral stability analysis for periodic traveling wave solutions of NLS and CGL perturbations. (English) Zbl 1148.35086 Physica D 237, No. 13, 1750-1772 (2008). MSC: 35Q55 35Q72 35P05 35B10 35B35 37K45 PDFBibTeX XMLCite \textit{T. Ivey} and \textit{S. Lafortune}, Physica D 237, No. 13, 1750--1772 (2008; Zbl 1148.35086) Full Text: DOI arXiv
Le Coz, Stefan; Fukuizumi, Reika; Fibich, Gadi; Ksherim, Baruch; Sivan, Yonatan Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential. (English) Zbl 1147.35356 Physica D 237, No. 8, 1103-1128 (2008). MSC: 35Q55 35B35 81Q10 82B10 PDFBibTeX XMLCite \textit{S. Le Coz} et al., Physica D 237, No. 8, 1103--1128 (2008; Zbl 1147.35356) Full Text: DOI arXiv Link