Inverse scattering and integrable systems



Invited articles:
abstract download 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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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)





Regular articles:
abstract download 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)
abstract download 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 , accepted (2017)
abstract download 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)
abstract download 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)
abstract download 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)
abstract download D.E. Pelinovsky and Y. Shimabukuro, Orbital stability of Dirac solitons, Letters in Mathematical Physics 104, 21-41 (2014)
abstract download A. Contreras and D.E. Pelinovsky, Stability of multi-solitons in the cubic NLS equation, Journal of Hyperbolic Differential Equations 11, 329-353 (2014)
abstract download T. Mizumachi and D. Pelinovsky, Backlund transformation and L2-stability of NLS solitons, International Mathematics Research Notices 2012, 2034-2067 (2012)
abstract download 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)
abstract download D. Pelinovsky and D. Wu, Gauge transformation and spectral decomposition for the Ishimori-II equations, J. Phys. A: Math. Gen. 36, 5557-5574 (2003)
abstract download 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)
abstract download D. Pelinovsky and C. Sulem, Spectral Decomposition for Dirac System Associated to the DSII Equation, Inverse Problems 16, 59-74 (2000)
abstract download D.E. Pelinovsky and C. Sulem, Bifurcations of new eigenvalues for the Benjamin-Ono equation, J. Math. Phys. 39, 6552-6572 (1998)
abstract download 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)
abstract download 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)
abstract download 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)
abstract download 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)
abstract download D.E.Pelinovsky and R.H.J.Grimshaw, A Spectral Transform for the Intermediate Nonlinear Shrodinger Equation, J.Math.Phys. 36, 4203-4219 (1995)
abstract download 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)
abstract download 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)
no abstract download D.E. Pelinovsky and Yu.A. Stepanyants, New Multisoliton Solutions of the Kadomtsev-Petviashvili Equation, JETP Lett. 57, 24-28 (1993)





Proceedings papers:
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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)
abstract download 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)
abstract download 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)
abstract download D. Pelinovsky, On a Structure of the Explicit Solutions to the Davey - Stewartson Equations, Physica D 87, 115-122 (1995)