My main research interests are in existence, stability, and global dynamics of nonlinear waves in dispersive wave equations, lattice differential equations, and diffusion-advection equations. These topics involve aplied harmonic analysis, PDE theory, spectral analysis, dynamical systems, asymptotic analysis, numerical methods. Slides of presentations at conferences and seminars are available in the reverse chronological order.
| Title | Year | Coauthors | Conference | Lecture |
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| Breathers on the periodic traveling wave background in the BO and NLS-BO dispersive equations | 2024 | J. Chen |
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| Stability of solitary waves in the NLS equation with a regularized and intensity-dependent dispersion | 2024 | M. Plum, P. Kevrekidis, R. Ross |
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| Stability and interactions of algebraic solitons in the massive Thirring model | 2024 | C. He, J. Han, ZQ. Li |
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| Pinning phenomenon for existence and stability of wave patterns | 2024 | G. Medvedev, L. Bengel, W. Reichel |
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| Traveling waves in the Babenko equation for water waves | 2024 | S. Locke |
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| Dispersive hydrodynamics in the modified KdV equation | 2024 | J. Chen, S. Cui, A. Mucalica, M. Hoefer, L. K. Arruda |
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| Instability of peaked waves in hydrodynamical models | 2024 | A. Geyer, F. Natali, S. Lafortune, S. Locke, Y. Liu |
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| Traveling waves in the Camassa–Holm equations: their stability and instability | 2024 | A. Geyer, F. Natali, S. Lafortune, Y. Liu |
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| Existence of breathers (modulating pulses) in periodic systems via spatial dynamics | 2024 | C. Chong, T. Dohnal, G. Schneider |
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| Domain walls with and without external potentials | 2023 | A. Contreras, M. Plum, V. Slastikov |
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| Instability of peaked traveling waves in the Camassa–Holm models | 2023 | A. Geyer, F. Natali, S. Lafortune |
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| Solitons and breathers on the periodic wave background | 2023 | M. Hoefer, A. Mucalica |
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| Dynamics of shocks in the modular Burgers equation | 2023 | P. Poullet, B. de Rijk |
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| Rogue waves arising on the periodic waves of the Ablowitz–Ladik equation | 2023 | J. Chen |
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| Justification of the KdV, KP-II, and Toda equations from the Fermi-Pasta-Ulam particle system | 2023 | G. Schneider |
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| Solitary waves under intensity-dependent dispersion | 2022 | M. Plum, P. Kevrekidis, R. Ross |
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| Periodic waves in discrete MKDV equation: modulational instability and rogue waves | 2022 | J. Chen |
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| Periodic and double periodic waves in NLS: existence and stability | 2022 | J. Chen |
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| Justification of the KP-II approximation in dynamics of two-dimensional FPU systems | 2022 | N. Hristov, G. Schneider |
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| Exponentially small splitting for heteroclinic and homoclinic orbits in lattice equations | 2022 | G. Alfimov |
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| Stability of smooth travelling waves and instability of peaked travelling waves in the Camassa–Holm models | 2022 | A. Geyer, F. Natali, S. Lafortune |
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| Domain walls in harmonic potentials | 2022 | A. Contreras, V. Slastikov |
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| Stability of smooth and peaked periodic waves in the Camassa-Holm equation | 2021 | A. Geyer, F. Natali |
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| Ground states of the energy super-critical Gross-Pitaevskii equation with harmonic potential | 2021 | Piotr Bizon, Szymon Sobieszek |
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| Variational characterization of periodic waves in the fractional KdV equation | 2021 | U. Le, F. Natali |
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| Solitary waves under intensity-dependent dispersion | 2021 | P. Kevrekidis, R. Ross |
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| Instability of breathers and double periodic waves in NLS | 2021 | M. Haragus |
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| Rogue waves on the background of periodic solutions of the DNLS equation | 2021 | J. Chen, J. Upsal |
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| Existence and stability of Klein-Gordon breathers in the small-amplitude limit | 2021 | J. Cuevas, P. Kevrekidis, T. Penati, S. Paleari |
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| Standing waves on quantum graphs: variational methods and the period function | 2020 | A. Kairzhan, R. Marangell, D. Noja |
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| Periodic waves in integrable equations: modulation instability and rogue waves | 2020 | J. Chen, R. White |
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| Instability of peaked waves in the Camassa-Holm equation | 2020 | F. Natali, A. Madiyeva |
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| "Periodic waves in the fractional KdV equation" | 2019 | F. Natali, U.Le |
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| "Instability of peaked waves" | 2019 | A. Geyer, F. Natali |
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| "Rogue waves on the periodic and double-periodic background" | 2019 | J. Chen, R. White |
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| "Drift and instability of steady states" | 2019 | A. Kairzhan, R. Goodman |
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| "Stationary states on metric graphs in the limit of large mass" | 2018 | G. Berkolaiko, J. Marzuola |
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| "Integrable semi-discretizations of integrable PDEs" | 2018 | N. Joshi |
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| "Krein signature in PT-symmetric systems" | 2018 | A. Chernyavsky |
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| "Instability of peaked periodic waves in reduced Ostrovsky equations" | 2018 | A. Geyer |
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| "Rogue waves on the periodic background" | 2018 | J. Chen |
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| "Bifurcations of self-similar solutions for reversing interface" | 2018 | J. Foster |
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| "Stability of domain walls in coupled systems" | 2017 | S. Alama, L. Bronsard, A. Contreras, M. Plum |
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| "Ground state of the conformal flow on three-sphere" | 2017 | P. Bizon |
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| "Inverse scattering for the massive Thirring model" | 2017 | A. Saalmann, Y. Shimabukuro |
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| "Nonlinear instability of half-solitons on star graphs" | 2017 | A. Kairzhan |
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| "Bifurcations of multi-vortex configurations in rotating BECs" | 2017 | C. Garcia-Azpeitia |
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| "Stability of nonlinear waves in integrable Hamiltonian PDEs" | 2017 |
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| "Transverse stability of periodic waves in KP-II" | 2017 | M. Haragus |
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| "Spectral stability of periodic waves in reduced Ostrovsky equations" | 2017 | E.Johnson, A. Geyer |
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| "Logarithmic Korteweg-De Vries equation" | 2017 |
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| "Self-similar solutions for reversing interface in the slow diffusion equation" | 2016 | J. Foster |
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| "Stability of breathers in nonlinear lattices" | 2016 | J. Cuevas and P. Kevrekidis |
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| "Nonlinear Schrodinger equation on the periodic graph" | 2016 | G. Schneider |
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| "Ground states on the bounded and unbounded graphs" | 2016 | J. Marzuola |
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| "Hamiltonian PT-symmetric chains of coupled pendula" | 2016 | A. Chernyavsky |
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| "Well-posedness and stability in integrable systems" | 2015 | Y. Shimabukuro |
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| "Heteroclinic orbits for travelling kinks in difference and nonlocal wave equations" | 2015 | G.L. Alfimov |
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| "Approximations of dynamics of nonlinear lattices on the extended time scale" | 2015 | A. Khan, T. Penati, S. Paleari |
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| "Global solutions and wave breaking in the reduced Ostrovsky equation" | 2015 | R. Grimshaw |
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| "Existence and stability of standing waves of the NLS equation on the tadpole graph" | 2015 | D. Noja, G. Shaikhova |
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| "Stability of Dirac solitons" | 2015 | Y. Shimabukuro |
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| "Stability of periodic waves and black solitons in the cubic defocusing NLS equation" | 2014 | Th. Gallay |
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| "Nonlinear dynamics in PT-symmetric lattices" | 2014 |
P. Kevrekidis V. Konotop I. Barashenkov |
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| "Thomas-Fermi ground state in a PT-symmetric confining potential" | 2014 | C. Gallo |
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| "Justification of the log-KdV equation for granular chains" | 2014 | E. Dumas |
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| "Orbital stability of Gaussian solitons in the log-KdV equation" | 2014 | R. Carles |
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| "Orbital stability of Dirac (MTM) solitons" | 2013 | Y. Shimabukuro |
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| "Validity of the weakly nonlinear solution for the Boussinesq-Ostrovsky equation" | 2013 | K. Khusnutdinova |
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| "Gaussian solitary waves in granular crystals" | 2013 | G. James |
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| "Bifurcations and resonance of breathers in the discrete Klein-Gordon equation" | 2013 | A.Sakovich |
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| "Spectral stability of nonlinear waves in KdV equations" | 2013 |
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| "Nonlinear states in PT-symmetric lattices" | 2013 | P. Kevrekidis |
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| "On transverse stability of discrete solitons" | 2012 | J. Yang |
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| "Periodic travelling waves in diatomic granular chains" | 2012 | M. Betti |
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| "Variational approximations in discrete nonlinear Schrodinger equations" | 2012 | C. Chong |
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| "Bifurcations of asymmetric vortices in symmetric harmonic potentials" | 2012 | P.G. Kevrekidis |
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| "Enstrophy growth in the viscous Burgers equation" | 2012 |
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| "Justification of the short-pulse equation" | 2011 | G. Schneider |
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| "Nonlinear Dirac equations in one spatial dimension" | 2011 | A. Stefanov |
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| "Polychromatic solitary waves in the periodic nonlinear Maxwell equations" | 2011 | G. Simpson, M. Weinstein |
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| "Propagation failure in the discrete Nagumo equation" | 2011 | H.J. Hupkes, B. Sandstede |
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| "Multi-site breathers in Klein-Gordon lattices: bifurcations, stability, and resonances" | 2011 | A.Sakovich |
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| "Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation" | 2011 | A.Sakovich |
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| "Backlund transformation and L2-stability of NLS solitons" | 2011 | T. Mizumachi |
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| "Wave breaking in the Ostrovsky-Hunter equation" | 2010 |
Y. Liu A. Sakovich |
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| "Vortices in a harmonic potential" | 2010 | P. Kevrekidis |
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| "Excited states in a harmonic potential" | 2010 | P. Kevrekidis |
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| "Symmetry-breaking bifurcations in a double-well potential" | 2010 | E. Kirr, P. Kevrekidis |
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| "Global well-posedness and wave breaking in the short-pulse equation" | 2010 |
Y. Liu A. Sakovich |
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| "Breathers from infinity in the anti-continuum limit" | 2009 | G. James |
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| "Justification of the DNLS equation for sign-varying nonlinearities" | 2009 | J. Belmonte-Beitia |
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| "Ground states in a harmonic potential" | 2009 | C. Gallo |
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| "Asymptotic stability of discrete solitons" | 2009 | A. Stefanov |
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| "Spectrum of an advection-diffusion operator" | 2008 | M.Chugunova |
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| "Localized modes in NLS lattices" | 2008 | P. Panayotaros, A. Stefanov |
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| "Eigenvalues of nonlinear ground state in the Thomas-Fermi approximation" | 2008 | C. Gallo |
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| "Justification of tight-binding approximation in nonlinear Schrodinger lattices" | 2008 |
R. MacKay G. Schneider |
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| "Localized traveling waves in nonlinear Schrodinger lattices" | 2007 |
T. Melvin A. Champneys |
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| "Hamiltonian lattice for nonlinear waves with parabolic potentials" | 2007 | P. Kevrekidis |
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| "Coupled-mode equations and gap solitons in two dimensions" | 2007 |
T. Dohnal, G. Schneider |
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| "Moving gap solitons in periodic potentials" | 2007 | G. Schneider |
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| "Justification of coupled-mode equations for gap solitons" | 2007 | G. Schneider |
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| "Dark solitons in external potentials" | 2007 | P. Kevrekidis |
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| "Stability of incompressible viscous fluid flows in a spherical shell" | 2007 | R. Ibragimov |
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| "Translationally invariant discrete NLS equation" | 2006 |
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| "Transverse instabilities of deep-water solitary waves" | 2006 | B. Deconinck |
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| "Multi-component vortices in coupled NLS equations" | 2006 | A. Desyatnikov |
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| "Two-pulse solutions in fifth-order KdV equation" | 2006 | M. Chugunova |
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| "Nonlinearity management in time-periodic NLS systems" | 2006 |
P. Kevrekidis, V. Zharnitsky |
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| "Moving kink in discrete phi-4 models" | 2005 |
O. Oxtoby, I. Barashenkov |
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| "Photonic crystals, coupled-mode equations and gap solitons" | 2005 |
D. Agueev M. Chugunova |
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| "Existence and stability of dark solitons in external potentials" | 2005 | D. Franzeskakis |
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| "Persistence and stability of discrete vortices in NLS lattices" | 2005 | P. Kevrekidis |
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| "Spectrum of the linearized NLS problem" | 2005 |
S. Cuccagna, V. Vougalter |
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| "Evans function for Lax operators with algebraic potentials" | 2005 | M. Klaus |
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| "Iteration method for nonlinear wave equations" | 2004 | Yu. Stepanyants |
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| "Solitons and vortices in discrete NLS equations" | 2004 | P. Kevrekidis |
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| "Spectrum of embedded solitons in the third-order NLS equation" | 2004 | J. Yang |
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| "Bifurcations of travelling wave solutions in discrete NLS equations" | 2004 | V. Rothos |
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| "Spectral stability of KdV solitons" | 2004 | Yu. Kodama |
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| "Bifurcations of gap solitons in periodic potentials" | 2003 |
A. Sukhorukov, Yu. Kivshar |
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| "Parametric resonance and radiative decay of dispersion-managed solitons" | 2003 |
V. Zharnitsky, J. Yang |
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