LeFloch, Philippe G.; Oliver, Jesús; Tsutsumi, Yoshio Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model. (English) Zbl 07791418 J. Evol. Equ. 23, No. 4, Paper No. 75, 28 p. (2023). MSC: 35B40 35L52 35L71 PDFBibTeX XMLCite \textit{P. G. LeFloch} et al., J. Evol. Equ. 23, No. 4, Paper No. 75, 28 p. (2023; Zbl 07791418) Full Text: DOI arXiv
Lührmann, Jonas; Schlag, Wilhelm Asymptotic stability of the sine-Gordon kink under odd perturbations. (English) Zbl 07783729 Duke Math. J. 172, No. 14, 2715-2820 (2023). Reviewer: Michał Kowalczyk (Santiago de Chile) MSC: 35B35 35C08 35L71 PDFBibTeX XMLCite \textit{J. Lührmann} and \textit{W. Schlag}, Duke Math. J. 172, No. 14, 2715--2820 (2023; Zbl 07783729) Full Text: DOI arXiv Link
Chen, Xuantao; Lindblad, Hans Asymptotics and scattering for wave Klein-Gordon systems. (English) Zbl 1528.35146 Commun. Partial Differ. Equations 48, No. 9, 1102-1147 (2023). MSC: 35Q53 35Q75 83C05 35R30 35L55 35B40 35C20 PDFBibTeX XMLCite \textit{X. Chen} and \textit{H. Lindblad}, Commun. Partial Differ. Equations 48, No. 9, 1102--1147 (2023; Zbl 1528.35146) Full Text: DOI arXiv
Liu, Xuan; Zhang, Ting Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime. (English) Zbl 07758698 Nonlinearity 36, No. 12, 6324-6363 (2023). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q55 35Q41 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{X. Liu} and \textit{T. Zhang}, Nonlinearity 36, No. 12, 6324--6363 (2023; Zbl 07758698) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya; Scrobogna, Stefano Small energy stabilization for 1D nonlinear Klein Gordon equations. (English) Zbl 1508.35142 J. Differ. Equations 350, 52-88 (2023). MSC: 35Q55 35A01 35A02 35B35 PDFBibTeX XMLCite \textit{S. Cuccagna} et al., J. Differ. Equations 350, 52--88 (2023; Zbl 1508.35142) Full Text: DOI arXiv
Li, Yongming; Lührmann, Jonas Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry. (English) Zbl 1503.35201 J. Differ. Equations 344, 172-202 (2023). MSC: 35Q51 35Q53 35B40 35B35 35B06 35A01 35A02 PDFBibTeX XMLCite \textit{Y. Li} and \textit{J. Lührmann}, J. Differ. Equations 344, 172--202 (2023; Zbl 1503.35201) Full Text: DOI arXiv
Cuccagna, Scipio; Maeda, Masaya Asymptotic stability of kink with internal modes under odd perturbation. (English) Zbl 1500.35038 NoDEA, Nonlinear Differ. Equ. Appl. 30, No. 1, Paper No. 1, 47 p. (2023). MSC: 35B40 35L71 37K40 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{M. Maeda}, NoDEA, Nonlinear Differ. Equ. Appl. 30, No. 1, Paper No. 1, 47 p. (2023; Zbl 1500.35038) 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
Germain, Pierre; Pusateri, Fabio Quadratic Klein-Gordon equations with a potential in one dimension. (English) Zbl 1495.35126 Forum Math. Pi 10, Paper No. e17, 172 p. (2022). MSC: 35L71 35P25 35Q56 42B37 PDFBibTeX XMLCite \textit{P. Germain} and \textit{F. Pusateri}, Forum Math. Pi 10, Paper No. e17, 172 p. (2022; Zbl 1495.35126) Full Text: DOI arXiv
Ballesteros, Miguel; Iniesta, Diego; Naumkin, Ivan; Peña, Clemente Wave and scattering operators for the nonlinear Klein-Gordon equation on a quarter-plane. (English) Zbl 1507.35229 J. Differ. Equations 321, 66-98done, nur noch checkmatrix und matrixtex (2022). MSC: 35Q53 35Q55 35B40 35P25 PDFBibTeX XMLCite \textit{M. Ballesteros} et al., J. Differ. Equations 321, 66--98done, nur noch checkmatrix und matrixtex (2022; Zbl 1507.35229) Full Text: DOI
Cazenave, Thierry; Naumkin, Ivan Local smooth solutions of the nonlinear Klein-Gordon equation. (English) Zbl 1479.35570 Discrete Contin. Dyn. Syst., Ser. S 14, No. 5, 1649-1672 (2021). MSC: 35L71 35L15 35L60 35A01 35B65 PDFBibTeX XMLCite \textit{T. Cazenave} and \textit{I. Naumkin}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 5, 1649--1672 (2021; Zbl 1479.35570) Full Text: DOI arXiv
Segata, Jun-Ichi Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension. (English) Zbl 1473.35058 Hokkaido Math. J. 50, No. 2, 187-205 (2021). MSC: 35B40 35L15 35L71 81Q05 PDFBibTeX XMLCite \textit{J.-I. Segata}, Hokkaido Math. J. 50, No. 2, 187--205 (2021; Zbl 1473.35058) Full Text: DOI Link
Lindblad, Hans; Lührmann, Jonas; Soffer, Avy Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities. (English) Zbl 1475.35305 Arch. Ration. Mech. Anal. 241, No. 3, 1459-1527 (2021). MSC: 35Q53 35B40 35B05 35P25 35C08 PDFBibTeX XMLCite \textit{H. Lindblad} et al., Arch. Ration. Mech. Anal. 241, No. 3, 1459--1527 (2021; Zbl 1475.35305) Full Text: DOI arXiv
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio; Van Den Bosch, Hanne A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models. (English) Zbl 1469.35150 Ann. PDE 7, No. 1, Paper No. 10, 98 p. (2021). MSC: 35L71 35B35 35B40 37K40 PDFBibTeX XMLCite \textit{M. Kowalczyk} et al., Ann. PDE 7, No. 1, Paper No. 10, 98 p. (2021; Zbl 1469.35150) Full Text: DOI arXiv
Lindblad, Hans; Lührmann, Jonas; Soffer, Avy Decay and asymptotics for the one-dimensional Klein-Gordon equation with variable coefficient cubic nonlinearities. (English) Zbl 1455.35021 SIAM J. Math. Anal. 52, No. 6, 6379-6411 (2020). MSC: 35B40 35L71 35L15 35P25 35Q51 35Q56 PDFBibTeX XMLCite \textit{H. Lindblad} et al., SIAM J. Math. Anal. 52, No. 6, 6379--6411 (2020; Zbl 1455.35021) Full Text: DOI arXiv
Naumkin, Ivan Modified scattering for the mixed initial-boundary problem for the nonlinear Klein-Gordon equation. (English) Zbl 1435.35222 Nonlinearity 33, No. 1, 276-324 (2020). Reviewer: Denis Borisov (Ufa) MSC: 35L20 35L71 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{I. Naumkin}, Nonlinearity 33, No. 1, 276--324 (2020; Zbl 1435.35222) Full Text: DOI
Masaki, Satoshi; Segata, Jun-Ichi Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions. (English) Zbl 1404.35299 Trans. Am. Math. Soc. 370, No. 11, 8155-8170 (2018). MSC: 35L71 35B40 81Q05 35L15 PDFBibTeX XMLCite \textit{S. Masaki} and \textit{J.-I. Segata}, Trans. Am. Math. Soc. 370, No. 11, 8155--8170 (2018; Zbl 1404.35299) Full Text: DOI arXiv
Germain, Pierre; Pusateri, Fabio; Rousset, Frédéric The nonlinear Schrödinger equation with a potential. (English) Zbl 1406.35355 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 6, 1477-1530 (2018). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q55 35B34 35P25 35B40 42A38 PDFBibTeX XMLCite \textit{P. Germain} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 6, 1477--1530 (2018; Zbl 1406.35355) Full Text: DOI arXiv
Masaki, Satoshi; Segata, Jun-ichi Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions. (English) Zbl 1397.35154 Commun. Pure Appl. Anal. 17, No. 4, 1595-1611 (2018). MSC: 35L71 35B40 81Q05 PDFBibTeX XMLCite \textit{S. Masaki} and \textit{J.-i. Segata}, Commun. Pure Appl. Anal. 17, No. 4, 1595--1611 (2018; Zbl 1397.35154) Full Text: DOI arXiv
Muñoz, Claudio; Poblete, Felipe; Pozo, Juan C. Scattering in the energy space for Boussinesq equations. (English) Zbl 1398.35203 Commun. Math. Phys. 361, No. 1, 127-141 (2018). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q53 35Q35 35P25 PDFBibTeX XMLCite \textit{C. Muñoz} et al., Commun. Math. Phys. 361, No. 1, 127--141 (2018; Zbl 1398.35203) Full Text: DOI arXiv
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio On asymptotic stability of nonlinear waves. (English) Zbl 1475.35415 Sémin. Laurent Schwartz, EDP Appl. 2016-2017, Exp. No. 18, 27 p. (2017). MSC: 35R30 35B35 35P25 35Q53 35Q55 35-02 PDFBibTeX XMLCite \textit{M. Kowalczyk} et al., Sémin. Laurent Schwartz, EDP Appl. 2016--2017, Exp. No. 18, 27 p. (2017; Zbl 1475.35415) Full Text: DOI
Kim, Donghyun A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension. (English) Zbl 1378.35201 Differ. Equ. Dyn. Syst. 25, No. 3, 431-451 (2017). MSC: 35L71 35L70 35B40 35L15 PDFBibTeX XMLCite \textit{D. Kim}, Differ. Equ. Dyn. Syst. 25, No. 3, 431--451 (2017; Zbl 1378.35201) Full Text: DOI arXiv
Chae, Myeongju; Oh, Sung-Jin Small data global existence and decay for relativistic Chern-Simons equations. (English) Zbl 1383.81134 Ann. Henri Poincaré 18, No. 6, 2123-2198 (2017). Reviewer: Sergiy Koshkin (Houston) MSC: 81T13 70H40 81S22 58J28 PDFBibTeX XMLCite \textit{M. Chae} and \textit{S.-J. Oh}, Ann. Henri Poincaré 18, No. 6, 2123--2198 (2017; Zbl 1383.81134) Full Text: DOI arXiv
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio Nonexistence of small, odd breathers for a class of nonlinear wave equations. (English) Zbl 1384.35109 Lett. Math. Phys. 107, No. 5, 921-931 (2017). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q51 35Q55 PDFBibTeX XMLCite \textit{M. Kowalczyk} et al., Lett. Math. Phys. 107, No. 5, 921--931 (2017; Zbl 1384.35109) Full Text: DOI arXiv
Kowalczyk, Michał; Martel, Yvan; Muñoz, Claudio Kink dynamics in the \(\phi^4\) model: asymptotic stability for odd perturbations in the energy space. (English) Zbl 1387.35419 J. Am. Math. Soc. 30, No. 3, 769-798 (2017). Reviewer: Joseph Shomberg (Providence) MSC: 35L71 35Q51 37K40 35B35 35L15 PDFBibTeX XMLCite \textit{M. Kowalczyk} et al., J. Am. Math. Soc. 30, No. 3, 769--798 (2017; Zbl 1387.35419) Full Text: DOI arXiv
Naumkin, Ivan Neumann problem for the nonlinear Klein-Gordon equation. (English) Zbl 1355.35141 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 149, 81-110 (2017). MSC: 35L71 35L20 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{I. Naumkin}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 149, 81--110 (2017; Zbl 1355.35141) Full Text: DOI
Delort, Jean-Marc Semiclassical microlocal normal forms and global solutions of modified one-dimensional KG equations. (Formes normales semi-classiques et solutions globales d’équations de Klein-Gordon modifiées en dimension un.) (English. French summary) Zbl 1377.35200 Ann. Inst. Fourier 66, No. 4, 1451-1528 (2016). Reviewer: Chengbo Wang (Hangzhou) MSC: 35L71 35A01 35B40 35A27 PDFBibTeX XMLCite \textit{J.-M. Delort}, Ann. Inst. Fourier 66, No. 4, 1451--1528 (2016; Zbl 1377.35200) Full Text: DOI
Sagawa, Yuji; Sunagawa, Hideaki The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension. (English) Zbl 1351.35191 Discrete Contin. Dyn. Syst. 36, No. 10, 5743-5761 (2016); corrigendum ibid. 40, No. 7, 4577-4578 (2020). MSC: 35Q55 35B40 PDFBibTeX XMLCite \textit{Y. Sagawa} and \textit{H. Sunagawa}, Discrete Contin. Dyn. Syst. 36, No. 10, 5743--5761 (2016; Zbl 1351.35191) Full Text: DOI arXiv
Sterbenz, Jacob Dispersive decay for the 1D Klein-Gordon equation with variable coefficient nonlinearities. (English) Zbl 1339.35191 Trans. Am. Math. Soc. 368, No. 3, 2081-2113 (2016). MSC: 35L71 35P25 35L15 35B34 PDFBibTeX XMLCite \textit{J. Sterbenz}, Trans. Am. Math. Soc. 368, No. 3, 2081--2113 (2016; Zbl 1339.35191) Full Text: DOI arXiv
Lindblad, Hans; Soffer, Avy Scattering for the Klein-Gordon equation with quadratic and variable coefficient cubic nonlinearities. (English) Zbl 1328.35201 Trans. Am. Math. Soc. 367, No. 12, 8861-8909 (2015). MSC: 35Q53 35B65 PDFBibTeX XMLCite \textit{H. Lindblad} and \textit{A. Soffer}, Trans. Am. Math. Soc. 367, No. 12, 8861--8909 (2015; Zbl 1328.35201) Full Text: DOI arXiv
Ionescu, Alexandru D.; Pusateri, Fabio Global solutions for the gravity water waves system in 2d. (English) Zbl 1325.35151 Invent. Math. 199, No. 3, 653-804 (2015). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35Q31 76B15 35Q35 35R35 PDFBibTeX XMLCite \textit{A. D. Ionescu} and \textit{F. Pusateri}, Invent. Math. 199, No. 3, 653--804 (2015; Zbl 1325.35151) Full Text: DOI arXiv
Kim, Donghyun; Sunagawa, Hideaki Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities. (English) Zbl 1284.35070 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 97, 94-105 (2014). MSC: 35B40 35L15 35L71 PDFBibTeX XMLCite \textit{D. Kim} and \textit{H. Sunagawa}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 97, 94--105 (2014; Zbl 1284.35070) Full Text: DOI arXiv
Berikelashvili, G.; Jokhadze, O.; Kharibegashvili, S.; Midodashvili, B. Finite difference solution of a nonlinear Klein-Gordon equation with an external source. (English) Zbl 1215.65138 Math. Comput. 80, No. 274, 847-862 (2011). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 35L70 35Q40 65M12 PDFBibTeX XMLCite \textit{G. Berikelashvili} et al., Math. Comput. 80, No. 274, 847--862 (2011; Zbl 1215.65138) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. The initial value problem for the quadratic nonlinear Klein-Gordon equation. (English) Zbl 1201.81048 Adv. Math. Phys. 2010, Article ID 504324, 35 p. (2010). MSC: 81Q05 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, Adv. Math. Phys. 2010, Article ID 504324, 35 p. (2010; Zbl 1201.81048) Full Text: DOI EuDML
Hayashi, Nakao; Naumkin, Pavel I. Final state problem for the cubic nonlinear Klein-Gordon equation. (English) Zbl 1283.35056 J. Math. Phys. 50, No. 10, 103511, 14 p. (2009). MSC: 35L71 81Q05 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, J. Math. Phys. 50, No. 10, 103511, 14 p. (2009; Zbl 1283.35056) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. Scattering operator for nonlinear Klein-Gordon equations. (English) Zbl 1182.35198 Commun. Contemp. Math. 11, No. 5, 771-781 (2009). MSC: 35Q53 35L70 35A22 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, Commun. Contemp. Math. 11, No. 5, 771--781 (2009; Zbl 1182.35198) Full Text: DOI
Taflin, Erik Simple nonlinear Klein-Gordon equations in two space dimensions, with long-range scattering. (English) Zbl 1123.35081 Lett. Math. Phys. 79, No. 2, 175-192 (2007). Reviewer: Viorel Iftimie (Bucureşti) MSC: 35Q75 35P25 35L70 74J20 PDFBibTeX XMLCite \textit{E. Taflin}, Lett. Math. Phys. 79, No. 2, 175--192 (2007; Zbl 1123.35081) Full Text: DOI arXiv
Delort, Jean-Marc Global existence and asymptotics for the quasilinear Klein-Gordon equation with small data in one space dimension. (Existence globale et comportement asymptotique pour l’équation de Klein-Gordon quasi linéaire à données petites en dimension 1.) (French. English summary) Zbl 1109.35095 Ann. Sci. Éc. Norm. Supér. (4) 39, No. 2, 335-345 (2006). MSC: 35Q40 35S50 35Q53 35B40 PDFBibTeX XMLCite \textit{J.-M. Delort}, Ann. Sci. Éc. Norm. Supér. (4) 39, No. 2, 335--345 (2006; Zbl 1109.35095) Full Text: DOI Numdam EuDML