A. B. Shabat

7.5k total citations · 2 hit papers
82 papers, 4.6k citations indexed

About

A. B. Shabat is a scholar working on Statistical and Nonlinear Physics, Geometry and Topology and Mathematical Physics. According to data from OpenAlex, A. B. Shabat has authored 82 papers receiving a total of 4.6k indexed citations (citations by other indexed papers that have themselves been cited), including 61 papers in Statistical and Nonlinear Physics, 14 papers in Geometry and Topology and 13 papers in Mathematical Physics. Recurrent topics in A. B. Shabat's work include Nonlinear Waves and Solitons (55 papers), Nonlinear Photonic Systems (39 papers) and Quantum chaos and dynamical systems (11 papers). A. B. Shabat is often cited by papers focused on Nonlinear Waves and Solitons (55 papers), Nonlinear Photonic Systems (39 papers) and Quantum chaos and dynamical systems (11 papers). A. B. Shabat collaborates with scholars based in Russia, Spain and United States. A. B. Shabat's co-authors include В. Е. Захаров, R. I. Yamilov, А. В. Михайлов, Luis Martı́nez Alonso, А. П. Веселов, V. É. Adler, N. Kh. Ibragimov, A. N. Leznov, А. В. Жибер and В. Г. Смирнов and has published in prestigious journals such as Communications in Mathematical Physics, Physics Letters A and Physica D Nonlinear Phenomena.

In The Last Decade

A. B. Shabat

69 papers receiving 4.1k citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media

1970 1.7k citations В. Е. Захаров, A. B. Shabat Journal of Experimental and Theoretical Physics profile →
A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I

1974 583 citations В. Е. Захаров, A. B. Shabat Functional Analysis and Its Applications profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
A. B. Shabat Russia	25	4.0k	1.3k	1.1k	1.0k	463	82	4.6k
V. B. Matveev Russia	25	5.4k 1.4×	1.8k 1.3×	1.1k 1.0×	1.5k 1.5×	347 0.7×	82	5.8k
Jarmo Hietarinta Finland	31	3.2k 0.8×	1.1k 0.8×	375 0.3×	1.3k 1.3×	328 0.7×	105	3.8k
M. A. Ablowitz United Kingdom	1	4.3k 1.1×	1.1k 0.9×	717 0.7×	986 1.0×	416 0.9×	2	4.5k
Dmitry E. Pelinovsky Canada	39	4.8k 1.2×	2.9k 2.2×	1.7k 1.6×	263 0.3×	281 0.6×	244	6.0k
Clifford S. Gardner United States	17	4.8k 1.2×	1.6k 1.2×	1.4k 1.3×	725 0.7×	593 1.3×	22	5.9k
Peter A. Clarkson United Kingdom	35	8.1k 2.1×	1.9k 1.4×	1.3k 1.2×	2.1k 2.1×	1.1k 2.3×	105	8.9k
А. В. Михайлов Russia	24	2.1k 0.5×	594 0.4×	411 0.4×	866 0.9×	217 0.5×	124	2.6k
D. Levi Italy	33	2.8k 0.7×	553 0.4×	292 0.3×	775 0.8×	596 1.3×	160	3.2k
Xianguo Geng China	37	4.9k 1.2×	1.1k 0.8×	655 0.6×	1.7k 1.7×	469 1.0×	249	4.9k
Engui Fan China	42	8.3k 2.1×	1.5k 1.2×	1.2k 1.1×	2.0k 2.0×	1.0k 2.2×	222	8.6k

Countries citing papers authored by A. B. Shabat

Since Specialization

Citations

This map shows the geographic impact of A. B. Shabat's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by A. B. Shabat with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites A. B. Shabat more than expected).

Fields of papers citing papers by A. B. Shabat

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by A. B. Shabat. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by A. B. Shabat. The network helps show where A. B. Shabat may publish in the future.

Co-authorship network of co-authors of A. B. Shabat

This figure shows the co-authorship network connecting the top 25 collaborators of A. B. Shabat. A scholar is included among the top collaborators of A. B. Shabat based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with A. B. Shabat. A. B. Shabat is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

Shabat, A. B., et al.. (2020). Darboux System and Separation of Variables in the Goursat Problem for a Third Order Equation in ℝ3. Russian Mathematics. 64(4). 35–43. 2 indexed citations

Shabat, A. B.. (2015). Difference Schrödinger equation and quasisymmetric polynomials. Theoretical and Mathematical Physics. 184(2). 1067–1077. 1 indexed citations

Shabat, A. B., et al.. (2012). Two-sided Darboux transformations. Theoretical and Mathematical Physics. 173(2). 1507–1517. 3 indexed citations

Adler, V. É., et al.. (2007). Модельное уравнение теории солитонов. Теоретическая и математическая физика. 153(1). 29–45. 3 indexed citations

Alonso, Luis Martı́nez, et al.. (2004). Гидродинамические редукции и решения универсальной иерархии. Теоретическая и математическая физика. 140(2). 216–229. 8 indexed citations

Adler, V. É. & A. B. Shabat. (1998). First integrals of generalized Toda chains. Theoretical and Mathematical Physics. 115(3). 639–646. 4 indexed citations

Shabat, A. B. & R. I. Yamilov. (1997). To a transformation theory of two-dimensional integrable systems. Physics Letters A. 227(1-2). 15–23. 53 indexed citations

Adler, V. É., I. T. Habibullin, & A. B. Shabat. (1997). Boundary value problem for the KDV equation on a half-line. Theoretical and Mathematical Physics. 110(1). 78–90. 16 indexed citations

Веселов, А. П. & A. B. Shabat. (1993). Dressing chains and the spectral theory of the Schrödinger operator. Functional Analysis and Its Applications. 27(2). 81–96. 168 indexed citations

10.

Leznov, A. N., A. B. Shabat, & R. I. Yamilov. (1993). Canonical transformations generated by shifts in nonlinear lattices. Physics Letters A. 174(5-6). 397–402. 44 indexed citations

11.

Михайлов, А. В. & A. B. Shabat. (1986). Integrable deformations of the Heisenberg model. Physics Letters A. 116(4). 191–194. 28 indexed citations

12.

Соколов, В. В. & A. B. Shabat. (1980). (L,A)-Pairs and a Ricatti type substitution. Functional Analysis and Its Applications. 14(2). 148–150. 17 indexed citations

13.

Ibragimov, N. Kh. & A. B. Shabat. (1980). Infinite Lie-Beklund algebras. Functional Analysis and Its Applications. 14(4). 313–315. 36 indexed citations

14.

Жибер, А. В. & A. B. Shabat. (1979). KLEIN-GORDON EQUATIONS WITH A NONTRIVIAL GROUP. Soviet physics. Doklady. 24. 607–609. 41 indexed citations

15.

Жибер, А. В., N. Kh. Ibragimov, & A. B. Shabat. (1979). Liouville type equations. 249(1). 26–29. 2 indexed citations

16.

Ibragimov, N. Kh. & A. B. Shabat. (1979). The Korteweg-de Vries equation from the point of view of transformation groups. Soviet physics. Doklady. 24. 15. 2 indexed citations

17.

Shabat, A. B.. (1975). Inverse-scattering problem for a system of differential equations. Functional Analysis and Its Applications. 9(3). 244–247. 48 indexed citations

18.

Захаров, В. Е. & A. B. Shabat. (1974). A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I. Functional Analysis and Its Applications. 8(3). 226–235. 583 indexed citations breakdown →

19.

Захаров, В. Е. & A. B. Shabat. (1973). Interaction between solitons in a stable medium. Journal of Experimental and Theoretical Physics. 37. 823. 246 indexed citations

20.

Захаров, В. Е. & A. B. Shabat. (1970). Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media. Journal of Experimental and Theoretical Physics. 34. 62–69. 1693 indexed citations breakdown →

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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