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Invited articles: |
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S. Cui and D. E. Pelinovsky,
Stability of standing periodic waves in the massive Thirring model,
Studies in Applied Mathematics 154
(2025) e12789 (24 pages)
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J. Chen and D.E. Pelinovsky,
Bright and dark breathers of the Benjamin-Ono equation on the traveling periodic background,
Wave Motion 126 (2024) 103263 (10 pages)
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J. Chen and D.E. Pelinovsky,
Rogue waves arising on the standing periodic waves in the Ablowitz-Ladik equation,
Stud. Appl. Math. 152 (2024) 147-173
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D.E. Pelinovsky,
Instability of double-periodic solutions in
the nonlinear Schrodinger equation,
Frontiers in Physics, 9, 599146 (10 pages)
(2021)
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S. Cuccagna and D.E. Pelinovsky,
The asymptotic stability of solitons in the cubic
NLS equation on the line,
Applicable Analysis 93, 791-822
(2014)
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Regular articles: |
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J. Chen and D. E. Pelinovsky,
Traveling periodic waves and breathers in the nonlocal derivative NLS equation,
Nonlinearity 38
(2025) 075016 (39 pages)
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S. Cui and D. E. Pelinovsky,
Instability bands for periodic traveling waves in the modified Korteweg-de Vries equation,
Proc. R. Soc. A 481
(2025) 20240993 (18 pages)
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J. Han, C. He, and D. E. Pelinovsky,
Algebraic solitons in the massive Thirring model,
Physical Review E 110
(2024) 034202 (11 pages)
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A. Mucalica and D.E. Pelinovsky,
Dark breathers on a snoidal wave background in the defocusing MKDV equation
Lett. Math. Phys. 114
(2024)100 (28 pages)
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J. Chen and D.E. Pelinovsky,
Periodic waves in the discrete MKDV equation:
modulational instability and rogue waves,
Physica D 44 (2023) 133652 (16 pages)
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M. Hoefer, A. Mucalica, and D. E. Pelinovsky,
KdV breathers on cnoidal wave background,
J. Physics A: Mathem. Theor. 56 185701 (25 pages)
(2023)
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A. Mucalica and D.E. Pelinovsky,
Solitons on the rarefaction wave background via the Darboux transformation,
Proc. R. Soc. A 478 20220474 (17 pages)
(2022)
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M. Haragus and D.E. Pelinovsky,
Linear instability of breathers for the focusing nonlinear Schrodinger equation,
Journal of Nonlinear Science, 32 66 (40 pages)
(2022)
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J. Chen, D.E. Pelinovsky, and J. Upsal,
Modulational instability of periodic standing waves in the derivative NLS equation,
Journal of Nonlinear Science, 31 58 (32 pages)
(2021)
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J. Chen and D.E. Pelinovsky,
Rogue waves on the background of periodic standing waves
in the derivative nonlinear Schrodinger equation,
Physical Review E 103, 062206 (25 pages)
(2021)
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D.E. Pelinovsky and R.E. White,
Localized structures on librational and rotational travelling waves
in the sine-Gordon equation,
Proceedings A of Royal Society of London 476: 20200490 (18 pages)
(2020)
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J. Chen, D.E. Pelinovsky, and R.E. White,
Periodic standing waves in the focusing nonlinear Schrodinger
equation: Rogue waves and modulation instability,
Physica D 405 132378 (13 pages)
(2020)
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G. Xu, A. Chabchoub, D.E. Pelinovsky, and B. Kibler,
Observation of modulation instability and rogue breathers
on stationary periodic waves,
Physical Review Research, 2, 033528 (8 pages)
(2020)
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J. Chen, D.E. Pelinovsky, and R.E. White
Rogue waves on the double-periodic background in the focusing
nonlinear Schrodinger equation,
Physical Review E 100, 052219 (18 pages)
(2019)
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J. Chen and D.E. Pelinovsky,
Periodic travelling waves of the modified KdV
equation and rogue waves on the periodic background,
Journal of Nonlinear Science 29, 2797-2843
(2019)
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N. Joshi and D.E. Pelinovsky,
Integrable semi-discretization of the massive Thirring
system in laboratory coordinates,
Journal of Physics: Mathematical Theoretical 52,
03LT01 (12pp)
(2019)
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T. Xu and D.E. Pelinovsky,
Darboux transformation and soliton solutions of the semi-discrete massive Thirring model,
Physics Letters A 383, 125948 (14 pages)
(2019)
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J. Chen and D.E. Pelinovsky,
Rogue periodic waves in the focusing nonlinear Schrodinger equation,
Proceeding of Royal Society of London A, 474, 20170814 (18 pages)
(2018)
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J. Chen and D.E. Pelinovsky,
Rogue periodic waves in the modified KdV equation,
Nonlinearity 31 1955-1980
(2018)
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D.E. Pelinovsky and Y. Shimabukuro,
Existence of global solutions to the derivative NLS equation
with the inverse scattering transform method,
International Mathematics Research Notices 2018,
5663-5728
(2018)
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D.E. Pelinovsky, A. Saalmann, and Y. Shimabukuro,
The derivative NLS equation: global existence with solitons,
Dynamics of PDE 14, 271-294
(2017)
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M. Haragus, J. Li, and D.E. Pelinovsky,
Counting unstable eigenvalues in Hamiltonian spectral
problems via commuting operators,
Communications in Mathematical Physics 354, 247-268
(2017)
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A. Contreras, D.E. Pelinovsky, and Y. Shimabukuro,
L2 orbital stability of Dirac solitons in the massive Thirring model,
Communications in PDEs 41, 227-255
(2016)
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T. Gallay and D.E. Pelinovsky,
Orbital stability in the cubic defocusing NLS equation. Part I: Cnoidal periodic waves,
Journal of Differential Equations 258, 3607-3638
(2015)
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T. Gallay and D.E. Pelinovsky,
Orbital stability in the cubic defocusing NLS equation. Part II: The black soliton,
Journal of Differential Equations 258, 3639-3660
(2015)
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D.E. Pelinovsky and Y. Shimabukuro,
Orbital stability of Dirac solitons,
Letters in Mathematical Physics 104, 21-41
(2014)
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A. Contreras and D.E. Pelinovsky,
Stability of multi-solitons in the cubic NLS equation,
Journal of Hyperbolic Differential Equations 11, 329-353
(2014)
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T. Mizumachi and D. Pelinovsky,
Backlund transformation and L2-stability of NLS solitons,
International Mathematics Research Notices
2012, 2034-2067
(2012)
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M. Klaus, D.E. Pelinovsky, and V.M. Rothos,
Evans function for Lax operators with algebraically
decaying potentials,
J. Nonlin. Sci. 16,
1-44 (2006)
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D. Pelinovsky and D. Wu,
Gauge transformation and spectral decomposition
for the Ishimori-II equations,
J. Phys. A: Math. Gen.
36, 5557-5574
(2003)
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D. Pelinovsky and C. Sulem,
Eigenfunctions and Eigenvalues
for a Scalar Riemann - Hilbert Problem Associated
to Inverse Scattering,
Comm. Math. Phys.
208, 713-760
(2000)
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D. Pelinovsky and C. Sulem,
Spectral Decomposition
for Dirac System Associated to the DSII Equation,
Inverse Problems 16,
59-74 (2000)
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D.E. Pelinovsky and C. Sulem,
Bifurcations of new
eigenvalues for the Benjamin-Ono equation,
J. Math. Phys. 39,
6552-6572 (1998)
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D. Pelinovsky,
Rational Solutions of the KP Hierarchy and
the Dynamics of Their Poles. II. Construction of the Degenerate
Polynomial Solutions, J. Math. Phys.
39, 5377-5395
(1998)
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I.V. Barashenkov and D.E. Pelinovsky,
Exact Vortex Solutions of the Complex
Sine-Gordon Theory on the Plane,
Phys. Lett. B 436, 117-124
(1998)
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D. Pelinovsky, J. Springael, F. Lambert,
and I. Loris,
On Modified NLS, Kaup and NLBq Equations:
Differential Transformations and Bilinearization,
J. Phys. A: Math. Gen. 30,
8705-8717 (1997)
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D.E. Pelinovsky and R.H.J. Grimshaw,
Structural Transformation of Eigenvalues
for a Perturbed Algebraic Soliton Potential,
Phys. Lett. A 229,
165-172 (1997)
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D.E.Pelinovsky and R.H.J.Grimshaw,
A Spectral Transform
for the Intermediate Nonlinear Shrodinger Equation,
J.Math.Phys. 36, 4203-4219
(1995)
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V.M.Galkin, D.E.Pelinovsky, and
Yu.A.Stepanyants, The
Structure of the Rational Solutions to the Boussinesq equation,
Physica D 80, 246-255
(1995)
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D. Pelinovsky,
Rational Solutions of the
Kadomtsev - Petviashvili Hierarchy and the Dynamics of Their
Poles. I. New form of a general rational solution,
J.Math.Phys. 35, 5820-5830
(1994)
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D.E. Pelinovsky and Yu.A. Stepanyants,
New Multisoliton
Solutions of the Kadomtsev-Petviashvili Equation,
JETP Lett. 57, 24-28
(1993)
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Proceedings papers: |
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D.E. Pelinovsky and A. Saalmann,
Inverse scattering for the massive Thirring model,
Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
(Editors: P. Miller, P. Perry, J.C. Saut, and C. Sulem),
Fields Institute Communications 83 (Springer, New York, NY), 497-528
(2019)
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D.E. Pelinovsky and V.M. Rothos,
Evans function for the AKNS problem with algebraic solitons,
"Mathematical and numerical aspects of wave propagation: WAVES 2003",
Proceedings of the Sixth International Conference on Mathematical and Numerical
Aspects of Wave Propagation Held at Jyvaskyla, Finland, 30 June - 4 July 2003, Eds.
G.C. Cohen, E. Heikkola, P. Joly, P. Neittaanmaki,
Springer, 729-734 (2003)
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A.S. Fokas,
D.E. Pelinovsky, and C. Sulem,
Interaction of Lumps With a Line
Soliton for the DSII Equation, Physica D
152-153, 189-198 (2001)
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D.E. Pelinovsky and C. Sulem,
Embedded Solitons of the DSII Equation,
CRM Proceedings and Lecture Notes, 27,
edited by I.M. Sigal and C. Sulem,
135-145 (2001)
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D.E. Pelinovsky and C. Sulem,
Asymptotic Approximations of a New
Eigenvalue in Linear Problems Without a Threshold,
Theor. Mat. Phys. 122, 98-106
(2000)
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D. Pelinovsky,
On a Structure of the Explicit Solutions
to the Davey - Stewartson Equations, Physica D
87, 115-122 (1995)
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V.M. Galkin, D.E. Pelinovsky, and
Yu.A. Stepanyants,
On the Existence of Multisolitons
Described by the KP1 equation,
Oscillations and Waves in Distributive Media,
(Nizhny Novgorod Polytechnical
Institute Press), 15-19
(1992)
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