Joseph Krasil'shchik

Site: https://diffiety.mccme.ru/curvita/isk.htm

Special Issue in honour of Joseph Krasil'shchik 70th birthday

Publications in geometry of differential equations

• I. S. Krasil'shchik and O.I. Morozov, The Calogero-Bogoyavlenskii-Schiff breaking soliton equation: recursion operators and higher symmetries, J. Geom. Phys. 192 (2023), 104927, arXiv:2305.03931

• I. S. Krasil'shchik and O.I. Morozov, Lagrangian extensions of multi-dimensional integrable equations. I. The five-dimensional Martínez Alonso-Shabat equation, Anal.Math.Phys. 13 (2023), 2, arXiv:2207.07936

• I. S. Krasil'shchik and O.I. Morozov, The equation of filtration for real gases: group classification, exact solutions, conservation laws, and differential invariants, Lobachevskii J. Math. 43 (2022), 2781-2784, doi:10.1134/S1995080222130224

• I. S. Krasil'shchik, On recursion operators for symmetries of the Pavlov-Mikhalev equation, Lobachevskii J. Math. 43 (2022), 2757-2780, arXiv:2203.13045

• I. S. Krasil'shchik and A. M. Verbovetsky, Recursion operators in the cotangent covering of the rdDym equation, Anal.Math.Phys. 12 (2022), 1, arXiv:2106.06763

• V. Lychagin and J. Krasilshchik (eds.), Geometric analysis of nonlinear partial differential equations, MDPI, 2021, doi:10.3390/books978-3-0365-1047-7

• I. S. Krasil'shchik, Nonlocal conservation laws of PDEs possessing differential coverings, Symmetry 12 (2020), 1760 arXiv:2009.09489

• I. S. Krasil'shchik and P. Vojčák, On the algebra of nonlocal symmetries for the 4D Martínez Alonso-Shabat equation, J. Geom. Phys. 163 (2021), 104122, arXiv:2008.10281

• I. S. Krasil'shchik and V. V. Lychagin, Geometric study of gas behavior in a one-dimensional nozzle (the case of the van der Waals gas), Lobachevskii J. Math. 41 (2020), 2458-2465, arXiv:2004.03896

• I. Krasil'shchik, O.I. Morozov, and P. Vojčák, Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation, J. Geom. Phys. 146 (2019), 103519, arXiv:1902.09341

• I. Krasil'shchik and A. Sergyeyev, Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws, A. Ann. Henri Poincaré 20 (2019), 2699-2715, arXiv:1901.07527

• H. Baran, P. Blaschke, I.S. Krasil'shchik, M. Marvan, On symmetries of the Gibbons-Tsarev equation, J. Geom. Phys. 144 (2019), 54-80, arXiv:1811.08199

• Joseph Krasil'shchik, Alexander Verbovetsky, and Raffaele Vitolo, The symbolic computation of integrability structures for partial differential equations, Springer, 2017; http://gdeq.org/Symbolic_Book

• P. Holba, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Reductions of the universal hierarchy and rdDym equations and their symmetry properties, Lobachevskii J. Math. 39 (2018), 673-681, arXiv:1712.07063

• P. Holba, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, 2D reductions of the equation $u_{yy}=u_{tx}+u_{y}u_{xx}-u_{x}u_{xy}$ and their nonlocal symmetries, J. Nonlinear Math. Phys. 24 (2017), suppl. 1, 36-47, arXiv:1707.07645

• H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Nonlocal symmetries of integrable linearly degenerate equations: a comparative study, Theor. Math. Phys. 196 (2018), 1089–1110, arXiv:1611.04938; Russian original: Teor. Mat. Fiz. 196 (2018), 169-192, Mi tmf9452

• I. S. Krasil'shchik, A. Sergyeyev, and O. I. Morozov, Infinitely many nonlocal conservation laws for the $ABC$ equation with $A+B+C\neq 0$, Calc. Var. 55 (2016), 123, arXiv:1511.09430

• H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Coverings over Lax integrable equations and their nonlocal symmetries, Theor. Math. Phys. 188 (2016), 1273-1295, arXiv:1507.00897; Russian original: Teor. Mat. Fiz. 188 (2016), 361-385, Mi tmf9044

• I.S. Krasil'shchik and A. Sergyeyev, Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more, J. Geom. Phys. 97 (2015), 266-278, arXiv:1501.07171

• H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Integrability properties of some equations obtained by symmetry reductions, J. Nonlinear Math. Phys. 22 (2015), 210-232, arXiv:1412.6461

• H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Five-dimensional Lax-integrable equation, its reductions and recursion operator, Lobachevskii J. Math. 36 (2015), 225-233

• H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems, J. Nonlinear Math. Phys. 21 (2014), 643-671, arXiv:1407.0246

• I. Krasil'shchik, Integrability in differential coverings, J. Geom. Phys. 87 (2015), 296-304, arXiv:1310.1189

• H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák, Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations, J. Phys.: Conf. Ser. 482 (2014), 012002, arXiv:1309.7435

• Iosif Krasil'shchik, Alexander Verbovetsky, and Raffaele Vitolo, A unified approach to computation of integrable structures, Acta Appl. Math. 120 (2012), 199-218, arXiv:1110.4560

• Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky, and Raffaele Vitolo, On integrable structures for a generalized Monge-Ampère equation, Theor. Math. Phys. 171 (2012), 600-615, arXiv:1104.0258; Russian original: Teor. Mat. Fiz. 171 (2012), 208-224, Mi tmf8365

• Joseph Krasil'shchik and Alexander Verbovetsky, Geometry of jet spaces and integrable systems, J. Geom. Phys. 61 (2011), 1633-1674, arXiv:1002.0077

• P. Kersten, I. Krasil'shchik, A. Verbovetsky, and R. Vitolo, Integrability of Kupershmidt deformations, Acta Appl. Math. 109 (2010), 75-86, arXiv:0812.4902.

• P. Kersten, I. Krasil'shchik, A. Verbovetsky, and R. Vitolo, Hamiltonian structures for general PDEs, Differential Equations - Geometry, Symmetries and Integrability: The Abel Symposium 2008 (B. Kruglikov, V. Lychagin, and E. Straume, eds.), Abel Symposia 5, Springer, 2009, pp. 187-198, arXiv:0812.4895.

• V. A. Golovko, I. S. Krasil'shchik, and A. M. Verbovetsky, Variational Poisson-Nijenhuis structures for partial differential equations, Theor. Math. Phys. 154 (2008), 227-239, arXiv:0812.4684; Russian original: Teor. Mat. Fiz. 154 (2008), 268-282, Mi tmf6168.

• V. Golovko, P. Kersten, I. Krasil'shchik, and A. Verbovetsky, On integrability of the Camassa-Holm equation and its invariants, Acta Appl. Math. 101 (2008), arXiv:0812.4681.

• I. Krasil'shchik, Algebraic theories of brackets and related (co)homologies, Acta Appl. Math. 109 (2010), 137-150, arXiv:0812.4676.

• I. S. Krasil'shchik and B. S. Kruglikov (eds.), Algebra and geometry of PDEs, Springer, 2008, Acta Appl. Math. 101 (2008), no. 1-3.

• I. S. Krasil'shchik, Estestvennye nakrytiya i integriruemye sistemy, Symmetries: theoretical and methodological aspects, Astrakhan Univ., Astrakhan, 2007, pp. 46-53 (Russian).

• J. Krasil'shchik, Nonlocal geometry of PDEs and integrability, Symmetry and perturbation theory (G. Gaeta, R. Vitolo, and Walcher S., eds.), World Sci., 2007, pp. 100-108.

• A. M. Verbovetsky, V. A. Golovko, and I. S. Krasil'shchik, Skobka Li dlya nelokal'nykh tenej, Scientific Bulletin of MSTUCA 114 (2007), 9-23 (Russian), КиберЛенинка.

• P. H. M. Kersten and I. S. Krasil'shchik, The Cartan covering and complete integrability of the KdV-mKdV system, Constructive Algebra and Systems Theory (B. Hanzon and Hazewinkel M., eds.), Royal Netherlands Academy of Arts and Sciences, 2006, pp. 251-265.

• Paul Kersten, Iosif Krasil'shchik, and Alexander Verbovetsky, A geometric study of the dispersionless Boussinesq type equation, Acta Appl. Math. 90 (2006), 143-178, arXiv:nlin/0511012.

• I. S. Krasil'shchik, Prostoj metod dokazatel'stva lokal'nosti simmetrij evolyutsionnykh uravnenij, Scientific Bulletin of MSTUCA 91 (2005), 12-19 (Russian), КиберЛенинка.

• P. H. M. Kersten, I. Krasil'shchik, and A. Verbovetsky, The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies, Memorandum of the Twente University 1727 (2004).

• Paul Kersten, Iosif Krasil'shchik, and Alexander Verbovetsky, Nonlocal constructions in the geometry of PDE, Symmetry in nonlinear mathematical physics. Part 1, Inst. Math. NAS Ukr., Kiev, 2004, pp. 412-423.

• P. Kersten, I. Krasil'shchik, and A. Verbovetsky, (Non)local Hamiltonian and symplectic structures, recursions and hierarchies: a new approach and applications to the $N=1$ supersymmetric KdV equation, J. Phys. A 37 (2004), 5003-5019, arXiv:nlin/0305026.

• P. Kersten, I. Krasil'shchik, and A. Verbovetsky, Hamiltonian operators and $\ell ^{*}$-coverings, J. Geom. Phys. 50 (2004), 273-302, arXiv:math/0304245.

• P. Kersten, I. Krasil'shchik, and A. Verbovetsky, On the integrability conditions for some structures related to evolution differential equations, Acta Appl. Math. 83 (2004), 167-173, arXiv:math/0310451.

• Joseph Krasil'shchik (ed.), Geometry of PDE in action: zero-curvature representations, recursion operators, and control systems, Kluwer, 2004, Acta Appl. Math. 83 (2004), no. 1-2.

• I Krasil'shchik, The long exact sequence of a covering: three applications, Diffiety Inst. Preprint Series 6 (2003), DIPS 6/2003.

• I. S. Krasil'shchik, A. M. Verbovetsky, and P. H. M. Kersten, Nonlocal Hamiltonian, symplectic and recursion structures for $N=1$ supersymmetric KdV equation, Proc. Int. Conf. Kolmogorov and Contemporary Mathematics, 2003, pp. 817-818.

• P. H. M. Kersten, I. S. Krasil'shchik, and A. M. Verbovetsky, A geometric approach to Hamiltonian structures for evolution equations, Proc. Int. Conf. Kolmogorov and Contemporary Mathematics (Moscow), 2003, pp. 815-816.

• S. Igonin, P. H. M. Kersten, and I. Krasil'shchik, On symmetries and cohomological invariants of equations possessing flat representations, Differential Geom. Appl. 19 (2003), 319-342, arXiv:math/0301344.

• P. H. M. Kersten, I. S. Krasil'shchik, and A. M. Verbovetsky, An extensive study of the $N=1$ supersymmetric KdV equation, Memorandum of the Twente University 1656 (2002).

• P. H. M. Kersten and I. S. Krasil'shchik, From recursion operators to Hamiltonian structures. The factorization method, Memorandum of the Twente University 1624 (2002), Lectures delivered at the MRI Spring School “Frobenius Manifolds in Mathematical Physics”.

• Iosif Krasil'shchik, A simple method to prove locality of symmetry hierarchies, Diffiety Inst. Preprint Series 9 (2002), DIPS 09/2002.

• Joseph Krasil'shchik, Geometry of differential equations: a concise introduction, Acta Appl. Math. 72 (2002), 1-17.

• Paul Kersten and Joseph Krasil'shchik, Complete integrability of the coupled KdV-mKdV system, Lie groups, geometric structures and differential equations—one hundred years after Sophus Lie, Adv. Stud. Pure Math., vol. 37, Math. Soc. Japan, 2002, pp. 151-171, arXiv:nlin/0010041.

• Sergei Igonin and Joseph Krasil'shchik, On one-parametric families of Bäcklund transformations, Lie groups, geometric structures and differential equations—one hundred years after Sophus Lie (Kyoto/Nara, 1999), Adv. Stud. Pure Math., vol. 37, Math. Soc. Japan, Tokyo, 2002, pp. 99-114, arXiv:nlin/0010040.

• Joseph Krasil'shchik (ed.), Symmetries of differential equations and related topics, Kluwer, 2002, Acta Appl. Math. 72 (2002), no. 1-2.

• I. S. Krasil'shchik, Deformations and integrable systems, Proc. Conf. Differential Equations and Related Topics dedicated to 100th Anniversary of birthday of I. G. Petrovskii, MSU, Moscow, 2001.

• Joseph Krasil'shchik, On one-parametric families of Bäcklund transformations, Diffiety Inst. Preprint Series 1 (2000), DIPS 1/2000.

• Joseph Krasil'shchik, Integrability and supersymmetry, RIMS Kokyuroku 1150 (2000), 147-152.

• I. S. Krasil'shchik and P. H. M. Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, 2000.

• Joseph Krasil'shchik and Michal Marvan, Coverings and integrability of the Gauss-Mainardi-Codazzi equations, Acta Appl. Math. 56 (1999), 217-230, arXiv:solv-int/9812010.

• I. S. Krasil'shchik, Cohomological approach to Poisson structures on nonlinear evolution equations, Lobachevskii J. Math. 3 (1999), 127-145 (electronic).

• Joseph Krasil'shchik in collaboration with Barbara Prinari, Lectures on linear differential operators over commutative algebras. (The 1st Italian diffiety school, July, 1998), Diffiety Inst. Preprint Series 1 (1999), DIPS 1/99, local copy.

• I. S. Krasil'shchik and A. M. Verbovetsky, Gomologicheskie metody v geometrii differentsial'nykh uravnenij, IUM, Moscow, 1999, Lecture notes, (Russian).

• A. V. Bocharov, V. N. Chetverikov, S. V. Duzhin, N. G. Khor'kova, I. S. Krasil'shchik (editor), A. V. Samokhin, Yu. N. Torkhov, A. M. Verbovetsky, and A. M. Vinogradov (editor), Symmetries and conservation laws for differential equations of mathematical physics, AMS, 1999.

• I. S. Krasil'shchik and A. M. Vinogradov (eds.), Geometrical aspects of nonlinear differential equations, Kluwer, 1999, Acta Appl. Math. 56 (1999), no. 2-3.

• I. S. Krasil'shchik, Algebras with flat connections and symmetries of differential equations, Lie groups and Lie algebras. Their representations, generalisations and applications, Math. Appl., vol. 433, Kluwer, 1998, pp. 407-424.

• Joseph Krasil'shchik, Cohomology background in geometry of PDE, Secondary calculus and cohomological physics, Contemp. Math., vol. 219, AMS, 1998, pp. 121-139.

• I. S. Krasil'shchik, Symmetries and recursion operators for soliton equations, Nonlinearity and geometry, PWN, Warsaw, 1998, pp. 141-156.

• I. S. Krasil'shchik and A. M. Verbovetsky, Homological methods in equations of mathematical physics, Open Education & Sciences, Opava, 1998, arXiv:math/9808130.

• B. P. Komrakov, I. S. Krasil'shchik, G. L. Litvinov, and A. B. Sossinsky (eds.), Lie groups and Lie algebras. Their representations, generalisations and applications, Mathematics and its Applications, vol. 433, Kluwer, 1998.

• Marc Henneaux, Joseph Krasil'shchik, and Alexandre Vinogradov (eds.), Secondary calculus and cohomological physics, Contemporary Mathematics, vol. 219, AMS, 1998.

• I. S. Krasil'shchik, Algebraicheskie metody v teorii integriruemykh sistem, MSU, Moscow, 1997, Dr. Sci. Thesis (Russian).

• I. S. Krasil'shchik, Characteristics of linear differential operators over commutative algebras, Acta Appl. Math. 49 (1997), 257-269.

• I. S. Krasil'shchik, Poincaré $\delta$-lemma for smooth algebras, Acta Appl. Math. 49 (1997), 249-255.

• I. S. Krasil'shchik, Calculus over commutative algebras: a concise user guide, Acta Appl. Math. 49 (1997), 235-248.

• A. V. Bocharov, A. M. Verbovetsky, A. M. Vinogradov (editor), S. V. Duzhin, I. S. Krasil'shchik (editor), A. V. Samokhin, Yu. N. Torkhov, N. G. Khor'kova, and V. N. Chetverikov, Simmetrii i zakony sokhraneniya uravnenij matematicheskoj fiziki, Factorial, Moscow, 1997 (Russian), Second edition 2005.

• I. S. Krasil'shchik and A. M. Vinogradov (eds.), Algebraic aspects of differential calculus, Kluwer, 1997, Acta Appl. Math. 49 (1997), no. 3.

• I. S. Krasil'shchik, Poisson structures on nonlinear evolution equations, Memorandum of the Twente University 1320 (1996).

• I. S. Krasil'shchik, A supersymmetry approach to Poisson structures over differential equations, Differential geometry and applications, Masaryk Univ., Brno, 1996, pp. 381-391.

• P. H. M. Kersten and I. S. Krasil'shchik, Graded Frölicher-Nijenhuis brackets and the theory of recursion operators for super differential equations, The interplay between differential geometry and differential equations, Amer. Math. Soc. Transl. Ser. 2, vol. 167, AMS, 1995, pp. 91-129, Also: Memorandum of the Twente University, 1993, no. 1147.

• I. S. Krasil'shchik and P. H. M. Kersten, Graded differential equations and their deformations: a computational theory for recursion operators, Acta Appl. Math. 41 (1995), 167-191.

• I. S. Krasil'shchik, Notes on coverings and Bäcklund transformations, ESI Preprint 260 (1995).

• I. S. Krasil'shchik, Hamiltonian formalism and supersymmetry for nonlinear differential equations, ESI Preprint 257 (1995).

• P. H. M. Kersten and I. S. Krasil'shchik (eds.), Geometric and algebraic structures in differential equations, Kluwer, 1995, Papers from the Workshop on Algebra and Geometry of Differential Equations held in Enschede, 1993, Reprint of Acta Appl. Math. 41 (1995), no. 1-3.

• I. S. Krasil'shchik and P. H. M. Kersten, Deformations and recursion operators for evolution equations, Geometry in partial differential equations, World Sci., 1994, pp. 114-154, Also: Memorandum of the Twente University, 1992, no. 1104.

• I. S. Krasil'shchik, An algebraic model for characteristics of differential equations, ESI Preprint 48 (1993).

• I. S. Krasil'shchik, Lie algebra structures for the symmetries of differential equations possessing recursion operators, ESI Preprint 47 (1993).

• I. S. Krasil'shchik, Some new cohomological invariants of nonlinear differential equations. II, Russ. Math. 37 (1993), no. 2, 52-65, Russian original: Izv. Vyssh. Uchebn. Zaved. Mat. 1993, no. 2, 54-68.

• I. S. Krasil'shchik, Some new cohomological invariants of nonlinear differential equations. I, Russ. Math. 37 (1993), no. 1, 25-35, Russian original: Izv. Vyssh. Uchebn. Zaved. Mat. 1993, no. 1, 27-37.

• I. S. Krasil'shchik, Some new cohomological invariants for nonlinear differential equations, Differential Geom. Appl. 2 (1992), 307-350.

• I. S. Krasil'shchik, Differential operators of constant growth and Jacobi structures of infinite order, Publ. IRMA Lille 30 (1992), no. XI, 1-21.

• I. S. Krasil'shchik, Algebry deformatsij differentsial'nykh uravnenij i operatory rekursii, Proceedings XXX MIKKHiS Scientific Conference (Moscow), MIKKHiS, 1992, pp. 18-21 (Russian).

• I. S. Krasil'shchik, Supercanonical algebras and Schouten brackets, Math. Notes 49 (1991), no. 1, 50-54, Russian original: Mat. Zametki 49 (1991), no. 1, 70-76.

• I. S. Krasil'shchik and A. M. Vinogradov, Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations, Acta Appl. Math. 15 (1989), 161-209.

• I. S. Krasil'shchik, Schouten bracket and canonical algebras, Global analysis—studies and applications, III, Lecture Notes in Math., vol. 1334, Springer, 1988, pp. 79-110, Russian original: Global'nyj analiz i matematicheskaya fizika, Nov. Global'nom anal., Voronezh, 1987, 73-94.

• I. S. Krasil'shchik, Del'ta-lemma Puankare, Mimeographed notes, 1987.

• I. S. Krasil'shchik, Pochemu preobrazovaniya Beklunda obrazuyut gruppu?, Proceedings of the seminar on the algebra and geometry of differential equations (Moscow), MSU, 1986 (Russian).

• I. S. Krasil'shchik, V. V. Lychagin, and A. M. Vinogradov, Geometry of jet spaces and nonlinear partial differential equations, Gordon and Breach, 1986.

• A. M. Vinogradov, I. S. Krasil'shchik, and V. V. Lychagin, Vvedenie v geometriyu nelineinykh differentsialnykh uravnenii, Nauka, Moscow, 1986 (Russian).

• I. S. Krasil'shchik and A. M. Vinogradov, Nonlocal symmetries and the theory of coverings: an addendum to Vinogradov's “Local symmetries and conservation laws” [Acta Appl. Math. 2 (1984), 21-78], Acta Appl. Math. 2 (1984), 79-96.

• A. M. Vinogradov and I. S. Krasil'shchik, On the theory of nonlocal symmetries of nonlinear partial differential equations, Sov. Math. Dokl. 29 (1984), 337-341, Russian original: Dokl. Akad. Nauk SSSR 275 (1984), 1044-1049.

• A. M. Vinogradov, I. S. Krasil'shchik, and V. V. Lychagin, Geometriya nelineinykh differentsialnykh uravnenii, MIEM, Moscow, 1982 (Russian).

• A. M. Vinogradov and I. S. Krasil'shchik, A method of calculating higher symmetries of nonlinear evolutionary equations, and nonlocal symmetries, Sov. Math. Dokl. 22 (1980), 235-239, Russian original: Dokl. Akad. Nauk SSSR 253 (1980), 1289-1293.

• I. S. Krasil'shchik, Hamiltonian cohomology of canonical algebras, Sov. Math. Dokl. 21 (1980), 625-629, Russian original: Dokl. Akad. Nauk SSSR 251 (1980), 1306-1309.

• A. M. Vinogradov, I. S. Krasil'shchik, and V. V. Lychagin, Primenenie nelinejnykh differentsial'nykh uravnenij v grazhdanskoj aviatsii, MIIGA, Moscow, 1977 (Russian).

• A. M. Vinogradov and I. S. Krasil'shchik, What is Hamiltonian formalism?, Russ Math. Surv. 30 (1975), no. 1, 177-202, Russian original: Uspehi Mat. Nauk 30 (1975), no. 1, 173-198; also in Integrable systems: selected papers, London Math. Soc. Lect. Note Ser., 60, 1981, 241-266.

• I. S. Krasil'shchik, Gamil'tonov formalizm v kanonicheskikh kol'tsakh, Voronezh Winter Math. School, Voronezh State Univ., 1974, pp. 23-24 (Russian).