# Joseph Krasil'shchik

From Geometry of Differential Equations

Site: http://diffiety.ac.ru/curvita/isk.htm

## Publications in geometry of differential equations

- 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*, arXiv:1712.07063

- P. Holba, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák,
*2D reductions of the equation and their nonlocal symmetries*, arXiv:1707.07645

- H. Baran, I. S. Krasil'shchik, O. I. Morozov, and P. Vojčák,
*Nonlocal symmetries of Lax integrable equations: a comparative study*, arXiv:1611.04938

- I. S. Krasil'shchik, A. Sergyeyev, and O. I. Morozov,
*Infinitely many nonlocal conservation laws for the equation with*, Calc. Var.**55**(2016), 123

- 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, 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,
*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).

- 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).

- 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 supersymmetric KdV equation*, J. Phys. A**37**(2004), 5003-5019, arXiv:nlin/0305026.

- P. Kersten, I. Krasil'shchik, and A. Verbovetsky,
*Hamiltonian operators and -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 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 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 -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.*, Acta Appl. Math.**2**(1984), 21-78]**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).