539 39 24

050 351 84 23

70 351 84 23

[email protected]

1. Baku State University, Department of Applied Mathematics, Professor.
2. Ministry of Science and Education of the Republic of Azerbaijan, Institute of Mathematics and Mechanics
 

He studied direct and inverse problems of spectral analysis for the discrete Sturm-Liouville operator, the discrete Hill operator, and the discrete Dirac operator. For one-dimensional Schrödinger equations with increasing potential, he constructed transformation operators that satisfy the condition at infinity. He studied inverse spectral problems in various formulations for one-dimensional Schrödinger equations with increasing potential. Using spectral problems, he studied the dispersion of the zeros of Bessel functions with respect to the index. He studied the global solvability of the Cauchy problem for systems of nonlinear differential equations and the construction of a solution by the inverse spectral problem method.

1. Asymptotics of the solution to the Cauchy problem for a Toda chain with initial data of the step type // Theoretical and Mathematical Physics, 1999, v. 119, no. 3, pp. 429-440 
2. Transformation operators for the perturbed difference Hill equation and their application // Siberian Mathematical Journal, 2003, v. 44, no. 4, pp. 926-937. 
3. On a rapidly decreasing solution of the Cauchy problem for the Toda chain // Theoretical and Mathematical Physics, 2005, v. 142, no. 1, pp. 5-12.
4. On the integration of the initial-boundary value problem for the Volterra chain // Differential equations, 2005, v. 41, no. 8, pp. 1134-1136.
5. Fast decreasing solution of the initial boundary value problem for the Toda chain //Ukrainian Mathematical Journal, 2005, v.57, no.8, pp.1144-1152.
6. Method for integrating the Cauchy problem for a Langmuir chain with a divergent initial condition // Zh. Vychis.mat.i mat.fiz., 2005, v. 45, no. 9, p. 1639-1650.
7. Direct and inverse scattering problems for the perturbed difference Hill equation // Sbornik Mathematics, 2005, vol. 196, no. 10, pp. 137-160.
8. Inverse scattering problem for the Schrödinger difference operator specified on the half-axis // Reports of the Academy of Sciences (Russia), 2006, v. 409, no. 4, pp. 451-454.
9. Solution of the Cauchy problem for the Toda chain with limitingly periodic initial data, Mathematical Collection, 2008, v. 199, no. 3, pp. 133-142.
10. Initial-boundary value problem for the Voltaire chain on the half-axis with a zero boundary condition // Reports of the Academy of Sciences (Russia), 2008, v. 423, no. 2, pp. 170-172.
11. Inverse scattering problem for the perturbed difference Hill equation, Mathematical Notes, 2009, v. 85, no. 3, pp. 456-470.
12. Inverse scattering problem for the Dirac difference operator on the semi-axis,
Reports of the Academy of Sciences (Russia), 2009, v. 424, no. 5, p. 597-599
13.On one algorithm for solving the Cauchy problem for a Langmuir chain //Journal of computational mathematics and mathematical physics, 2009, v. 49, no. 9, pp. 1589-1594
14. On the conditions for the discreteness of the spectrum of a semi-infinite Jacobi matrix with a zero diagonal // Ukrainian Mathematical Journal, 2010, v. 57, no. 2, pp. 285-289
15. Cauchy problem for a semi-infinite Voltaire chain with an asymptotically periodic initial condition // Sibir. math. zhurn., 2010, v. 51, no. 2, pp. 926-937.
16.On the global solvability of the Cauchy problem for one infinite system of nonlinear differential equations//Differential equations, 2010, vol. 46, no. 2, pp. 113-116.17. 17. Inverse scattering problem for the discrete Sturm-Liouville operator on the entire axis // Reports of the Academy of Sciences (Russia), 2010, v. 431, no. 1, pp. 25-26
18. Solution Cauchy problems for a semi-infinite Toda chain in the class of Hilbert-Schmidt operators // Reports of the Academy of Sciences (Russia), 2010, v. 432, no. 4, p.
19. Inverse scattering problem for the perturbed difference Hill equation // Mathematical notes. 2009. v.85, no. 3, p.456-470.
20. Solution of the Cauchy problem for a semi-infinite Toda chain in the class of Hilbert-Schmidt operators // Reports of the Russian Academy of Sciences, 2010. v. 432, no. 4, pp. 456-457.
21. Spectral analysis of one class of Schrödinger difference operators // Reports of the Russian Academy of Sciences, 2011, v. 436, no. 6, pp. 731-732.
22. Inverse scattering problem for the discrete Sturm-Liouville equation // Mathematical Collection, 2011, v. 202, no. 7, pp. 147-160.
23. Integration of the Toda chain with stepwise initial data // Reports of the Russian Academy of Sciences, 2013, v. 448, no. 2, pp. 142-144.
24. Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice//Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 12, pp. 2008-2013.
25. The inverse scattering problem for a discrete Dirac system on the whole axis// Journal of Inverse and Ill-posed Problems, 2017, v.25, Issue 6, pp.829-834.
26. Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis // Theoretical and Mathematical Physics, 195:1 (2018), 54–63.
27. To the inverse scattering problem for the one-dimensional Schrödinger equation with increasing potential // Ukrainian Mathematical Journal, 2018, v. 70, no. 10, p. 1390-1402.
28. Transformation operators for a perturbed harmonic oscillator // Mathematical notes, 2019, vol. 105, no. 5, pp. 740-746.
29. Algorithm for solving the Cauchy problem for one infinite-dimensional system of nonlinear differential equations // Journal of Computational Mathematics and Mathematical Physics, 2019, v. 59, no. 2, p. 247-252
30. On the spectral properties of the one-dimensional Stark operator on the half-axis // Ukrainian Mathematical Journal, 2019, v. 71, no. 11, pp. 1579-1584.
31. Inverse spectral problem for the Schrodinger equation with an additional linear potential// Theoretical and Mathematical Physics, 202(1): 58–71 (2020).
32. On the transformation operator for the Schrödinger equation with an additional linear potential // Functional analysis and its applications, 2020, v. 54, no. 1, pp. 93–96.
33. On the zeros of the modified Bessel function of the second kind // Journal of Computational Mathematics and Mathematical Physics, 2020, volume 60, no. 5, p. 104–107.
34. Inverse spectral problem for the one-dimensional Stark operator on the half-axis // Ukrainian Mathematical Journal, 2020, v. 72, no. 4, pp. 494-508.35. Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition// J. Inverse Ill-Posed Problems, 2020. v.29,№5, 675-688.
36. One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis//Georgian Mathematical Journal, 2021, v.29, issue 2, pp.225-228.
37. One remark on the inverse scattering problem for the perturbed Hill equation // Mathematical Notes, 2022, volume 112, issue 2, 263–268.
38. On transformation operators for the Schrödinger equation with an additional periodic complex potential// Bol. Soc. Mat. Mex. (2023) 29:36 https://doi.org/10.1007/s40590-023-00508-0
39. Transformation operator for the Schrödinger equation with additional exponential potential // Izvestia Vuzov. Mathematics, 2023, No. 9, pp. 76-84
40. Inverse scattering problem for the Schrödinger equation with an additional growing potential on the entire axis // Theoretical and Mathematical Physics, 2023, volume 216, no. 1, pp. 117-132 https://doi.org/10.4213/tmf10476

He gives lectures and seminars at Baku State University and Azerbaijan University.