Mizumachi, Tetsu Linear stability of elastic \(2\)-line solitons for the KP-II equation. (English) Zbl 07776366 Q. Appl. Math. 82, No. 1, 115-226 (2024). MSC: 35B35 35C08 35Q35 35Q51 37K40 PDFBibTeX XMLCite \textit{T. Mizumachi}, Q. Appl. Math. 82, No. 1, 115--226 (2024; Zbl 07776366) Full Text: DOI arXiv
Vainchtein, Anna Solitary waves in FPU-type lattices. (English) Zbl 07529695 Physica D 434, Article ID 133252, 22 p. (2022). MSC: 82-XX 35-XX PDFBibTeX XMLCite \textit{A. Vainchtein}, Physica D 434, Article ID 133252, 22 p. (2022; Zbl 07529695) Full Text: DOI
Duran, Henry; Xu, Haitao; Kevrekidis, Panayotis G.; Vainchtein, Anna Unstable dynamics of solitary traveling waves in a lattice with long-range interactions. (English) Zbl 1521.35074 Wave Motion 108, Article ID 102836, 17 p. (2022). MSC: 35C08 PDFBibTeX XMLCite \textit{H. Duran} et al., Wave Motion 108, Article ID 102836, 17 p. (2022; Zbl 1521.35074) Full Text: DOI arXiv
Djoufack, Z. I.; Kenmogne, Fabien; Nguenang, J. P.; Kenfack-Jiotsa, A. Dynamics of solitons with periodic loops intrinsic localized modes and modulational instability in a quantum 2D nonlinear square Klein-Gordon chain. (English) Zbl 1496.35148 Chaos Solitons Fractals 142, Article ID 110403, 13 p. (2021). MSC: 35C08 35Q55 37K60 PDFBibTeX XMLCite \textit{Z. I. Djoufack} et al., Chaos Solitons Fractals 142, Article ID 110403, 13 p. (2021; Zbl 1496.35148) Full Text: DOI
Kolebaje, Olusola; Popoola, O. O.; Vincent, U. E. Occurrence of vibrational resonance in an oscillator with an asymmetric Toda potential. (English) Zbl 1483.78004 Physica D 419, Article ID 132853, 10 p. (2021). MSC: 78A60 37K10 37K60 34C15 65L06 PDFBibTeX XMLCite \textit{O. Kolebaje} et al., Physica D 419, Article ID 132853, 10 p. (2021; Zbl 1483.78004) Full Text: DOI Link
Liu, Yong; Wei, Juncheng Nondegeneracy, Morse index and orbital stability of the KP-I lump solution. (English) Zbl 1428.35458 Arch. Ration. Mech. Anal. 234, No. 3, 1335-1389 (2019). MSC: 35Q53 37K35 37B30 35C08 35C07 35P99 35B35 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{J. Wei}, Arch. Ration. Mech. Anal. 234, No. 3, 1335--1389 (2019; Zbl 1428.35458) Full Text: DOI
Herrmann, Michael; Matthies, Karsten Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains. (English) Zbl 1428.37070 Trans. Am. Math. Soc. 372, No. 5, 3425-3486 (2019). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 37K60 37K40 70H14 74H10 PDFBibTeX XMLCite \textit{M. Herrmann} and \textit{K. Matthies}, Trans. Am. Math. Soc. 372, No. 5, 3425--3486 (2019; Zbl 1428.37070) Full Text: DOI arXiv
Xu, Haitao; Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices. (English) Zbl 1402.37086 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2117, Article ID 20170192, 26 p. (2018). MSC: 37K60 37K40 35C07 35C08 PDFBibTeX XMLCite \textit{H. Xu} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2117, Article ID 20170192, 26 p. (2018; Zbl 1402.37086) Full Text: DOI arXiv
Liu, Yong; Wei, Juncheng Nondegeneracy of the traveling lump solution to the 2 + 1 Toda lattice. (English) Zbl 1404.37082 J. Math. Phys. 59, No. 10, 101501, 26 p. (2018). MSC: 37K10 35C07 35Q53 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{J. Wei}, J. Math. Phys. 59, No. 10, 101501, 26 p. (2018; Zbl 1404.37082) 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
Pego, Robert L.; Sun, Shu-Ming Asymptotic linear stability of solitary water waves. (English) Zbl 1362.35240 Arch. Ration. Mech. Anal. 222, No. 3, 1161-1216 (2016). Reviewer: Natalia Bondarenko (Saratov) MSC: 35Q35 76B25 35B35 35B40 76B15 PDFBibTeX XMLCite \textit{R. L. Pego} and \textit{S.-M. Sun}, Arch. Ration. Mech. Anal. 222, No. 3, 1161--1216 (2016; Zbl 1362.35240) Full Text: DOI arXiv
Contreras, Andres; Pelinovsky, Dmitry E.; Shimabukuro, Yusuke \(L^{2}\) orbital stability of Dirac solitons in the massive Thirring model. (English) Zbl 1342.35287 Commun. Partial Differ. Equations 41, No. 2, 227-255 (2016). MSC: 35Q41 35Q51 35Q75 37K10 37K45 37K15 35B35 PDFBibTeX XMLCite \textit{A. Contreras} et al., Commun. Partial Differ. Equations 41, No. 2, 227--255 (2016; Zbl 1342.35287) Full Text: DOI arXiv
Mizumachi, Tetsu Stability of line solitons for the KP-II equation in \(\mathbb {R}^2\). (English) Zbl 1329.35056 Mem. Am. Math. Soc. 1125, vii, 95 p. (2015). MSC: 35B35 37K40 35Q35 35C08 PDFBibTeX XMLCite \textit{T. Mizumachi}, Stability of line solitons for the KP-II equation in \(\mathbb {R}^2\). Providence, RI: American Mathematical Society (AMS) (2015; Zbl 1329.35056) Full Text: DOI arXiv
Kowalczyk, Michał; Liu, Yong; Wei, Juncheng Singly periodic solutions of the Allen-Cahn equation and the Toda lattice. (English) Zbl 1321.35054 Commun. Partial Differ. Equations 40, No. 2, 329-356 (2015). Reviewer: Satoshi Tanaka (Okayama) MSC: 35J61 35B10 PDFBibTeX XMLCite \textit{M. Kowalczyk} et al., Commun. Partial Differ. Equations 40, No. 2, 329--356 (2015; Zbl 1321.35054) Full Text: DOI Link
Mizumachi, Tetsu Asymptotic stability of \(N\)-solitary waves of the FPU lattices. (English) Zbl 1260.35170 Arch. Ration. Mech. Anal. 207, No. 2, 393-457 (2013). MSC: 35Q51 35C08 35B35 PDFBibTeX XMLCite \textit{T. Mizumachi}, Arch. Ration. Mech. Anal. 207, No. 2, 393--457 (2013; Zbl 1260.35170) Full Text: DOI arXiv
Mizumachi, Tetsu; Tzvetkov, Nikolay Stability of the line soliton of the KP-II equation under periodic transverse perturbations. (English) Zbl 1233.35174 Math. Ann. 352, No. 3, 659-690 (2012). MSC: 35Q53 35B35 35C08 35Q35 PDFBibTeX XMLCite \textit{T. Mizumachi} and \textit{N. Tzvetkov}, Math. Ann. 352, No. 3, 659--690 (2012; Zbl 1233.35174) Full Text: DOI arXiv
Benes, G. N.; Hoffman, A.; Wayne, C. E. Asymptotic stability of the Toda \(m\)-soliton. (English) Zbl 1226.82006 J. Math. Anal. Appl. 386, No. 1, 445-460 (2012). MSC: 82B20 37K10 37K35 37K40 37K45 PDFBibTeX XMLCite \textit{G. N. Benes} et al., J. Math. Anal. Appl. 386, No. 1, 445--460 (2012; Zbl 1226.82006) Full Text: DOI arXiv
Bambusi, Dario; Paleari, Simone; Penati, Tiziano Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein-Gordon lattices. (English) Zbl 1203.37121 Appl. Anal. 89, No. 9, 1313-1334 (2010). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37K50 34C25 65N30 37K60 PDFBibTeX XMLCite \textit{D. Bambusi} et al., Appl. Anal. 89, No. 9, 1313--1334 (2010; Zbl 1203.37121) Full Text: DOI arXiv
Mizumachi, Tetsu Asymptotic stability of lattice solitons in the energy space. (English) Zbl 1190.82023 Commun. Math. Phys. 288, No. 1, 125-144 (2009). MSC: 82C20 35Q51 37K60 PDFBibTeX XMLCite \textit{T. Mizumachi}, Commun. Math. Phys. 288, No. 1, 125--144 (2009; Zbl 1190.82023) Full Text: DOI arXiv