Kairzhan, Adilbek; Pelinovsky, Dmitry E. Nonlinear instability of half-solitons on star graphs. (English) Zbl 1392.35289 J. Differ. Equations 264, No. 12, 7357-7383 (2018). MSC: 35Q55 35C08 35B38 35B20 81Q35 PDFBibTeX XMLCite \textit{A. Kairzhan} and \textit{D. E. Pelinovsky}, J. Differ. Equations 264, No. 12, 7357--7383 (2018; Zbl 1392.35289) Full Text: DOI arXiv
Cuccagna, Scipio; Pelinovsky, Dmitry E. The asymptotic stability of solitons in the cubic NLS equation on the line. (English) Zbl 1457.35067 Appl. Anal. 93, No. 4, 791-822 (2014). MSC: 35Q55 37K15 37K35 37K40 35B35 35B40 35C08 PDFBibTeX XMLCite \textit{S. Cuccagna} and \textit{D. E. Pelinovsky}, Appl. Anal. 93, No. 4, 791--822 (2014; Zbl 1457.35067) Full Text: DOI arXiv
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
Kirr, E.; Kevrekidis, P. G.; Pelinovsky, D. E. Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials. (English) Zbl 1235.34128 Commun. Math. Phys. 308, No. 3, 795-844 (2011). Reviewer: Rodica Luca Tudorache (Iaşi) MSC: 34C23 34L05 34B40 35Q55 PDFBibTeX XMLCite \textit{E. Kirr} et al., Commun. Math. Phys. 308, No. 3, 795--844 (2011; Zbl 1235.34128) Full Text: DOI arXiv
Chugunova, Marina; Pelinovsky, Dmitry Count of eigenvalues in the generalized eigenvalue problem. (English) Zbl 1310.35212 J. Math. Phys. 51, No. 5, 052901, 19 p. (2010). MSC: 35Q55 35J60 35P30 35C07 37K10 PDFBibTeX XMLCite \textit{M. Chugunova} and \textit{D. Pelinovsky}, J. Math. Phys. 51, No. 5, 052901, 19 p. (2010; Zbl 1310.35212) Full Text: DOI arXiv
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