Contact Information
 me Mailing Address Mathematical division
B. Verkin ILTPE of NASU
47 Nauky Ave.
61103, Kharkiv, Ukraine
Office Mathematical division, Room 214
E-Mail iraegorova@gmail.com

Education and degrees
Habilitation "Inverse problem method and non decreasing solutions of nonlinear evolutionary equations", Institute of Mathematics, Kyiv, 2010.
PhD Thesis "Spectral analysis for Dirac operators and Jacobi matrices with limit periodic coefficients, which are fast approximated by periodic ones",
Kharkiv State University, 1987
(scientific adviser L. Pastur, ILTPE, Kharkiv).
Post-graduate Kharkiv State University (1982-1985).
Graduate Kharkiv State University (1977-1982),
Diploma with honour in Mathematics, 1982.
Research interests
• Inverse spectral analysis for differential and difference operators.
• Direct and inverse scattering theory.
• Nonlinear evolutionary equations: inverse scattering transform and long time asymptotics.
Employment
— since 2013: leading researcher, ILTPE, Kharkiv
— 2004-2013: senior researcher, ILTPE, Kharkiv
— 1999-2004: associate professor, Kharkiv National University
— 1989-1999: researcher, ILTPE, Kharkiv

Teaching
— Vector Calculus, Purdue University (Spring 2018)
— Partial Differential Equations Kharkiv National University (Fall 2016 and Spring 2017)
— Topics In Vector Calculus, Purdue University (Spring 2013)
— Inverse scattering transform, graduate level course, Kharkiv National University (Spring 2012, Spring 2017)
— Asymptotic evaluation of integrals, graduate level course, Kharkiv National University (Spring 2011)
— Applied asymptotic analysis, seminar for graduate students, Faculty of Mathematics, University of Vienna (Winter 2009-2010)
— Riemann surfaces and nonlinear equations, graduate level course, Kharkiv National University (Fall 2009)
— Introduction to inverse scattering theory and application, graduate level course, Faculty of Mathematics, University of Vienna (Winter 2008-2009)
— Introduction to inverse spectral problems, graduate level course, Faculty of Mathematics, University of Vienna (Spring 2007)
— Calculus I, Calculus II, Linear Algebra, Kharkiv National University (academic years 1999-2006)
— Calculus I, Calculus II, Kharkiv Polytechnic Institute ( academic year 1998-1999)

Research Articles in Journals
  1. Long-time asymptotics for the Toda shock problem: Non-overlapping spectra (with J. Michor and G. Teschl), Zh. Mat. Fiz. Anal. Geom. 3, 3-45 (2018). [PDF]
  2. Rarefaction waves for the Toda equation via nonlinear steepest descent (with J. Michor and G. Teschl), Discrete Contin. Dyn. Syst. 38, 2007-2028 (2018). [PDF]
  3. 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. 4, 325-343 (2017). [PDF]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. Dispersion estimates for one-dimensional discrete Schrödinger and wave equations (with E. Kopylova and G. Teschl), J. Spectr. Theory 5 (2015) 663-696. [PDF]
  11. 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]
  12. 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]
  13. 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.
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. Reconstruction of the transmission coefficient for steplike finite-gap backgrounds (with G. Teschl), Oper. Matrices, 3, no. 2 (2009) 205-214. [PDF]
  21. 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]
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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).
  27. 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]
  28. Discrete spectrum for complex perturbations of periodic Jacobi matrices (with L. Golinskii), J. Difference Equ. Appl., 11, no. 14 (2005) 1185-1203.
  29. 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).
  30. 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.
  31. Transformation operator for Jacobi matrices with asymptotically periodic coefficients (with A. Boutet - de Monvel), J. Difference Equ. Appl., 10, no. 8 (2004) 711-727.
  32. Jacobi operator with step-like asymptotically periodic coefficients (with J. Bazargan), Mat. Fiz. Anal. Geom. 10, no. 3 (2003) 425-442.
  33. The scattering problem for step-like Jacobi operator, Mat. Fiz. Anal. Geom., 9, no. 2 (2002) 188-205.
  34. The asymptotic solitons for Toda lattice in the resonance case, Nonlinear boundary problems, 11 (2001) 37–43.
  35. The Toda lattice with step-like initial data. Soliton asymptotics (with A. Boutet - de Monvel), Inverse Problems 16, no. 4, (2000) 955-977.
  36. On solutions of nonlinear Schr¨odinger equations with Cantor-type spectrum (with A. Boutet - de Monvel), J. Anal. Math., 72 (1997) 1-20.
  37. 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.
  38. 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).
  39. 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.
  40. Almost periodicity of some solutions of the KdV equation with Cantor spectrum, Dopov. Akad. Nauk Ukraine, no. 7 (1993) 26-29 (Russian).
  41. 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.
  42. 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.
  43. 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.
  44. Spectral analysis of Jacobi limit-periodic matrices, Dokl. Akad. Nauk Ukrain. SSR Ser. A, no. 3 (1987) 7-9 (Russian).
  45. Spectral properties of the Dirac operator with limit-periodic coefficients, Dokl. Akad. Nauk Ukrain. SSR Ser. A, no. 5 (1986) 10-13 (Russian).
  46. 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).