Approximations of nonlinear waves in lattices



Regular articles:
abstract download C. Chong, D. E. Pelinovsky, and G. Schneider, On the existence of generalized breathers and transition fronts in time-periodic nonlinear lattices, SIAM J. Appl. Dynam. Systems 24 (2025) 894--928
abstract download D.E. Pelinovsky and G. Schneider, KP-II approximation for a scalar FPU system on a 2D square lattice, SIAM J. Appl. Math. 83 (2023) 79-98
abstract download N. Hristov and D.E. Pelinovsky, Justification of the KP-II approximation in dynamics of two-dimensional FPU systems, Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP) 73 213 (26 pages) (2022)
abstract download H. Huh, S. Hussain, and D.E. Pelinovsky, Chern-Simons-Schrodinger theory on a one-dimensional lattice, Letters in Mathematical Physics 110, 2221-2244 (2020)
abstract download D.E. Pelinovsky and G. Schneider, The monoatomic FPU system as a limit of a diatomic FPU system, Applied Mathematics Letters 107, 106387 (8 pages) (2020)
abstract download D.E. Pelinovsky, On the linearized log-KdV equation, Communications in Mathematical Sciences 15, 863-880 (2017)
abstract download A. Khan and D. Pelinovsky, Long-time stability of small FPU solitary waves, Discrete Continuous Dynamical Systems Series A 37, 2065-2075 (2017)
abstract download D.E. Pelinovsky, T. Penati, and S. Paleari, Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrdoinger equations, Review in Mathematical Physics 28, 1650015 (25 pages) (2016)
abstract download E. Dumas and D.E. Pelinovsky, Justification of the log-KdV equation in granular chains: the case of precompression, SIAM J. Math. Anal. 46, 4075-4103 (2014)
abstract download R. Carles and D.E. Pelinovsky, On the orbital stability of Gaussian solitary waves in the log-KdV equation, Nonlinearity 27, 3185-3202 (2014)
abstract download G. James and D.E. Pelinovsky, Gaussian solitary waves and compactons in FPU lattices with Hertzian potentials, Proceedings of Royal Society A 470, 20130465 (20 pages) (2014)
abstract download M. Betti and D.E. Pelinovsky, Periodic travelling waves in dimer granular chains, Journal of Nonlinear Science 23, 689-711 (2013)
abstract download G. James and D. Pelinovsky, Breather continuation from infinity in nonlinear oscillator chains, Discrete and Continuous Dynamical Systems A 32, 1775-1799 (2012)





Proceedings papers:
abstract download D.E. Pelinovsky, T. Penati, and S. Paleari Existence and stability of Klein-Gordon breathers in the small-amplitude limit, Mathematics of Wave Phenomena, Editors: W. Dörfler, M. Hochbruck, D. Hundertmark, W. Reichel, A. Rieder, R. Schnaubelt, and B. Schörkhuber, Trends in Mathematics (Birkhäuser Basel) 251-278 (2020)