Preprints

- On the long-time asymptotics for the Korteweg-de Vries equation with steplike initial data associated with rarefaction waves, with K. Andreiev, Zh. Mat. Fiz. Anal. Geom. [PDF]
- Long-time asymptotics for the Toda shock problem: Non-overlapping spectra, with G. Teschl and J. Michor [PDF]
- Rarefaction waves for the Toda equation via nonlinear steepest descent, with G. Teschl and J. Michor, Discrete Contin. Dyn. Syst. [PDF]

Research Articles in Journals

- Uniqueness of the solution of the Riemann-Hilbert problem for the rarefaction wave of
the Korteweg-de Vries equation,
with K. Andreiev, DANU
**11**, 3-9 (2017). [PDF] - Rarefaction waves of the Korteweg-de Vries equation via nonlinear steepest descent (with K. Andreiev,
T.-L. Lange and G. Teschl) J. Differential Equations
**261**(2016) 5371-5410. [PDF] - Dispersion estimates for one-dimensional Schr¨odinger and Klein-Gordon equations revisited (with E.
Kopylova, V. Marchenko and G. Teschl) Russian Math. Surveys
**71**(2016) 3-26. [PDF] - On the form of dispersive shock waves of the Korteweg-de Vries equation (with Z. Gladka and G. Teschl) Zh. Mat. Fiz. Anal. Geom.
**12**(2016) 3-16. [PDF] - Properties of the scattering matrix and dispersion estimates for Jacobi operators (with M. Holzleitner and G. Teschl) J. Math. Anal. Appl. 434 (2016) 956-966. [PDF]
- Zero energy scattering for one-dimensional Schrödinger operators and applications to dispersive estimates (with M. Holzleitner and G. Teschl) Proc. Amer. Math. Soc. Ser. B 2 (2015) 51-59. [PDF]
- Dispersion estimates for one-dimensional discrete Schrödinger and wave equations (with E. Kopylova and G. Teschl) J. Spectr. Theory 5 (2015) 663-696. [PDF]
- Inverse scattering theory for Schr?dinger operators with steplike potentials (with Z. Gladka, T.-L. Lange and G. Teschl) Zh. Mat. Fiz. Anal. Geom 11 (2015) 123-158. [PDF]
- Long-time asymptotics for the Korteweg-de Vries equation with steplike initial data (with G. Teschl, Z. Gladka, and V. Kotlyarov) Nonlinearity 26 (2013) 1839-1864. [PDF]
- On the asymptotic properties of polynomials orthogonal with respect to varying weights and related problems of spectral theory (with L. Pastur) Algebra i Analiz 25 (2013), no. 2, 101–124 (Russian); translation in St. Petersburg Math. J. 25 (2014), no. 2, 223240.
- Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data (with J. Michor and G. Teschl), Math. Phys. Anal. Geom. 16 (2013) 111-136. [PDF]
- On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data II. Perturbations with finite moments (with G. Teschl), J. d’Analyse Math., 115 (2011) 71–101. [PDF]
- On the Cauchy problem for the modified Korteweg-de Vries
equation with steplike finite-gap initial data,
with G. Teschl,
Proceedings of the International Research Program on Nonlinear PDE, H. Holden and K. H. Karlsen (eds), Contemp. Math.
**526**, Amer. Math. Soc., Providence (2010) 151-158. [PDF] - A Paley-Wiener theorem for periodic scattering with applications to the Korteweg-de Vries equation (with G. Teschl), Zh. Mat. Fiz. Anal. Geom., 6, no. 1 (2010) 21-33. [PDF]
- Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds (with J. Michor and G. Teschl), J. Math. Phys., 50, no. 10 (2009), 103521, 9 pp. [PDF]
- On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data. I. Schwartz-type perturbations (with K. Grunert and G. Teschl), Nonlinearity, 22, no. 6 (2009) 1431- 1457. [PDF]
- Reconstruction of the transmission coefficient for steplike finite-gap backgrounds (with G. Teschl), Oper. Matrices, 3, no. 2 (2009) 205-214. [PDF]
- Soliton solutions of the Toda hierarchy on quasi-periodic backgrounds revisited (with J. Michor and G. Teschl), Math. Nachr., 282, no. 4 (2009) 526-539. [PDF]
- Inverse scattering theory for one-dimensional Schrdinger operators with steplike finite-gap potentials (with A. Boutet - de Monvel and G. Teschl), J. Anal. Math., 106 (2008) 271-316. [PDF]
- Scattering theory for Jacobi operators with general step-like quasiperiodic background (with J. Michor and G. Teschl), Zh. Mat. Fiz. Anal. Geom., 4, no. 1 (2008) 33-62. [PDF]
- Scattering theory for Jacobi operators with a steplike quasi-periodic background (with J. Michor and G. Teschl), Inverse Problems, 23 , no. 3 (2007) 905-918. [PDF]
- Inverse scattering transform for the Toda hierarchy with quasi-periodic background (with J. Michor and G. Teschl), Proc. Amer. Math. Soc., no. 6 135 (2007) 1817-1827 (electronic). [PDF]
- The scattering problem for the Sturm-Liouville operator with a step-like asymptotically periodic potential( with J. Bazargan), Dopov. Nats. Akad. Nauk Ukr., no. 2 (2006) 7-12 (Russian).
- Scattering theory for Jacobi operators with quasi-periodic background (with J. Michor and G. Teschl), Comm. Math. Phys. 264, no. 3 (2006) 811-842. [PDF]
- Discrete spectrum for complex perturbations of periodic Jacobi matrices (with L. Golinskii), J. Difference Equ. Appl., 11, no. 14 (2005) 1185-1203.
- On the location of the discrete spectrum for complex Jacobi matrices (with L. Golinskii), Proc. Amer. Math. Soc., 133, no. 12 (2005) 3635-3641 (electronic).
- On limit sets for the discrete spectrum of complex Jacobi matrices (with L. Golinskii), Mat. Sb., 196, no. 6 (2005) 43–70 (Russian); translation in Sb. Math. 196, no. 5-6 (2005) 817-844.
- Transformation operator for Jacobi matrices with asymptotically periodic coefficients (with A. Boutet - de Monvel), J. Difference Equ. Appl., 10, no. 8 (2004) 711-727.
- Jacobi operator with step-like asymptotically periodic coefficients (with J. Bazargan), Mat. Fiz. Anal. Geom. 10, no. 3 (2003) 425-442.
- The scattering problem for step-like Jacobi operator, Mat. Fiz. Anal. Geom., 9, no. 2 (2002) 188-205.
- The asymptotic solitons for Toda lattice in the resonance case, Nonlinear boundary problems, 11 (2001) 37–43.
- The Toda lattice with step-like initial data. Soliton asymptotics (with A. Boutet - de Monvel), Inverse Problems 16, no. 4, (2000) 955-977.
- On solutions of nonlinear Schr¨odinger equations with Cantor-type spectrum (with A. Boutet - de Monvel), J. Anal. Math., 72 (1997) 1-20.
- Soliton asymptotics of the Cauchy problem solution for the Toda lattice (with A. Boutet - de Monvel and E. Khruslov) Inverse Problems 13, no. 2 (1997) 223-237.
- On the almost periodicity of ”reflectionless” Dirac operators with the Cantor spectrum (with A. Surkova), Dopov. Nats. Akad. Nauk Ukraine, no. 12 (1995) 13-15 (Russian).
- The Cauchy problem for the KdV equation with almost periodic initial data whose spectrum is nowhere dense, Spectral operator theory and related topics, Adv. Soviet Math., 19, Amer. Math. Soc., Providence, RI, 1994, 181-208.
- Almost periodicity of some solutions of the KdV equation with Cantor spectrum, Dopov. Akad. Nauk Ukraine, no. 7 (1993) 26-29 (Russian).
- On a class of almost periodic solutions of the KdV equation with a nowhere dense spectrum, Dokl. Akad. Nauk 323, no. 2 (1992) 219–222 (Russian); translation in Russian Acad. Sci. Dokl. Math. 45, no. 2 (1993) 290-293.
- Asymptotic behavior of solutions of the second boundary value problem in domains with random thin cracks (with E. Khruslov), Teor. Funktsii Funktsional. Anal. i Prilozhen, no. 52 (1989) 91–103 (Russian); translation in J. Soviet Math. 52, no. 5, (1990) 3412-3421.
- The complete set of spectral parameters of the Dirac operator with limit-periodic coefficients, Teor. Funktsii Funktsional. Anal. i Prilozhen, no. 47 (1987) 25–35 (Russian); translation in J. Soviet Math. 48, no. 6, (1990) 636-643.
- Spectral analysis of Jacobi limit-periodic matrices, Dokl. Akad. Nauk Ukrain. SSR Ser. A, no. 3 (1987) 7-9 (Russian).
- Spectral properties of the Dirac operator with limit-periodic coefficients, Dokl. Akad. Nauk Ukrain. SSR Ser. A, no. 5 (1986) 10-13 (Russian).
- Asymptotic behavior at low frequencies of the eigenvalue distribution of a disordered chain of atoms, Dokl. Akad. Nauk Ukrain. SSR Ser. A , no. 9 (1984) 9-12 (Russian).