` Dmitry Pelinovsky Web Page: Publication Bank

Stability of nonlinear waves



Invited papers:
abstract download D. Pelinovsky and J. Yang, Stability analysis of embedded solitons in the generalized third-order NLS equation, Chaos 15, 037115 (2005)
abstract download D.E. Pelinovsky and R.H.J. Grimshaw, Asymptotic Methods in Soliton Stability Theory, Advances in Fluid Mechanics Series, 12: Nonlinear Instability Analysis, edited by L.Debnath and S.R.Choudhury, (Computational Mechanics Publications, Southampton, Boston), 245-312 (1997)





Regular articles:
abstract download S. Alama, L. Bronsard, A. Contreras, and D.E. Pelinovsky, Domains walls in the coupled Gross-Pitaevskii equations, Archives for Rational Mechanics and its Applications 215, 579-610 (2015)
abstract download D.E. Pelinovsky and A. Stefanov, Asymptotic stability of small gap solitons in the nonlinear Dirac equations, Journal of Mathematical Physics 53, 073705 (27 pages) (2012)
abstract download M. Chugunova and D. Pelinovsky, Count of eigenvalues in the generalized eigenvalue problem, Journal of Mathematical Physics 51, 052901 (19 pages) (2010)
abstract download M. Chugunova and D. Pelinovsky, On quadratic eigenvalue problems arising in stability of discrete vortices, Linear Algebra and its Applications 431, 962-973 (2009)
abstract download M. Chugunova and D. Pelinovsky, Two-pulse solutions in the fifth-order KdV equation: rigorous theory and numerical approximations, Discrete and Continuous Dynamical Systems, Series B 8, 773-800 (2007)
abstract download A. Comech, S. Cuccagna, and D. Pelinovsky, Nonlinear instability of a critical traveling wave in the generalized Korteweg - de Vries equation, SIAM Journal on Mathematical Analysis 39, 1-33 (2007)
abstract download M. Chugunova and D. Pelinovsky, Block-diagonalization of the symmetric first-order coupled-mode system, SIAM Journal of Applied Dynamical Systems 5, 66-83 (2006)
abstract download V. Vougalter and D. Pelinovsky, Eigenvalues of zero energy in the linearized NLS problem, Journal of Mathematical Physics 47, 062701 (2006)
abstract download S. Cuccagna, D. Pelinovsky, and V. Vougalter, Spectra of positive and negative energies in the linearized NLS problem, Comm. Pure Appl. Math. 58 1-29 (2005)
abstract download S. Cuccagna and D. Pelinovsky, Bifurcations from the end points of the essential spectrum in the linearized NLS problem, J. Math. Phys. 46 053520 (2005)
abstract download D.E. Pelinovsky, Inertia law for spectral stability of solitary waves in coupled nonlinear Schrodinger equations, Proc. Roy. Soc. Lond. A 461 783-812 (2005)
abstract download D.E. Pelinovsky and J. Yang, Instabilities of multihump vector solitons in coupled nonlinear Schrodinger equations, Stud. Appl. Math. 115 109-137 (2005)
abstract download Y. Kodama and D. Pelinovsky, Spectral stability and time evolution of N solitons in KdV hierarchy, J. Phys. A: Math. Gen. 38 6129-6140 (2005)
abstract download A.Comech and D. Pelinovsky, Purely Nonlinear Instability of Standing Waves with Minimal Energy, Comm. Pure Appl. Math. 56 1565-1607 (2003)
abstract download Y. Tan, J. Yang, and D.E. Pelinovsky, Semi-stability of embedded solitons in the general fifth-order KdV equation, Wave Motion 36, 241-255 (2002)
abstract download D.E. Pelinovsky and J. Yang, A normal form for nonlinear resonance of embedded solitons, Proc. R. Soc. Lond. A 458, 1469-1497 (2002)





Proceedings papers:
abstract download D.E. Pelinovsky, Spectral stability of nonlinear waves in KdV-type evolution equations, "Nonlinear Physical Systems: Spectral Analysis, Stability, and Bifurcations" (Edited by O.N. Kirillov and D.E. Pelinovsky) (Wiley-ISTE, NJ) 377-400 (2014)
abstract download T. Mizumachi and D. Pelinovsky, On the asymptotic stability of localized modes in the discrete nonlinear Schrodinger equation, Discrete and Continuous Dynamical Systems Series S 5, 971-987 (2012)