Fetching the paper…
Reading the bibliography…
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given.
Ch. Riquier, Les systèmes d’équations aux dérivées partielles , Gauthier-Villars, 1910
1910
Earlier work this paper cites.
S. Lie, Gesammelte Abhandlungen , Teubner, 1922-–60, 7 volumes
1922
Earlier work this paper cites.
L. Bianchi, Lezioni di geometria differenziale , 3 ed., Zanichelli, 1927-30
1927
Earlier work this paper cites.
M. Janet, Leçons sur les systèmes d’équations aux dérivées partielles , Gauthier-Villars, 1929
1929
Earlier work this paper cites.
T. Lewis, Some special solutions of the equations of axially symmetric gravitational fields , Proc. Roy. Soc. London Ser. A 136
1932
Earlier work this paper cites.
E. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques , Hermann, Paris, 1946
1946
Earlier work this paper cites.
P. K. Rashevskii, The geometric theory of partial differential equations , OGIZ, Moscow-Leningrad, 1947, In Russian
1947
Earlier work this paper cites.
Ch. Ehresmann, Introduction à la théorie des structures infinitésimales et des pseudogroupes de Lie , Colloque de Topologie et Géométrie Différentielle, Strasbourg, 1952, no. 11, La Bibliothèque Nationale et Universitaire de Strasbourg, 1953
1953
Earlier work this paper cites.
Ch. Ehresmann, Introduction à la théorie des structures infinitésimales et des pseudogroupes de Lie , Géométrie Différentielle. Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1953, Centre National de la Recherche Scientifique, Paris, 1953
1953
Earlier work this paper cites.
P. M. Morse and H. Feshbach, Methods of theoretical physics , McGraw-Hill Book Co., 1953, 2 volumes
1953
Earlier work this paper cites.
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for solving the Korteweg-de Vries equation , Phys. Rev. Lett. 19
1967
Earlier work this paper cites.
H. Goldschmidt, Existence theorems for analytic linear partial differential equations , Ann. of Math. (2) 86
1967
Earlier work this paper cites.
R. M. Miura, Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation , J. Math. Phys. 9
1968
Earlier work this paper cites.
R. M. Miura, C. S. Gardner, and M. D. Kruskal, Korteweg-de Vries equation and generalizations. II. Existence of conservation laws and constants of motion , J. Math. Phys. 9
1968
Earlier work this paper cites.
D. C. Spencer, Overdetermined systems of linear partial differential equations , Bull. Amer. Math. Soc. 75
1969
Earlier work this paper cites.
C. H. Su and C. S. Gardner, Korteweg-de Vries equation and generalizations. III. Derivation of the Korteweg-de Vries equation and Burgers equation , J. Math. Phys. 10
1969
Earlier work this paper cites.
M. D. Kruskal, R.M. Miura, C. S. Gardner, and N. J. Zabusky, Korteweg-de Vries equation and generalizations. V. Uniqueness and nonexistence of polynomial conservation laws , J. Math. Phys. 11
1970
Earlier work this paper cites.
C. S. Gardner, Korteweg-de Vries equation and generalizations. IV. The Korteweg-de Vries equation as a Hamiltonian system , J. Mathematical Phys. 12
1971
Earlier work this paper cites.
R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons , Phys. Rev. Lett. 27
1971
Earlier work this paper cites.
V. E. Zakharov and L. D. Faddeev, The Korteweg-de Vries equation is a fully integrable Hamiltonian system , Funct. Anal. Appl. 5
1971
Earlier work this paper cites.
M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems , Studies in Appl. Math. 53
1974
Earlier work this paper cites.
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Korteweg-deVries equation and generalization. VI. Methods for exact solution , Comm. Pure Appl. Math. 27
1974
Earlier work this paper cites.
D. J. Kaup, A higher-order water-wave equation and the method for solving it , Progr. Theoret. Phys. 54
1975
Earlier work this paper cites.
H. D. Wahlquist and F. B. Estabrook, Prolongation structures of nonlinear evolution equations , J. Mathematical Phys. 16
1975
Earlier work this paper cites.
R. K. Dodd and R. K. Bullough, Bäcklund transformations for the sine-Gordon equations , Proc. Roy. Soc. London Ser. A 351
1976
Earlier work this paper cites.
H. D. Wahlquist and F. B. Estabrook, Prolongation structures of nonlinear evolution equations. II , J. Mathematical Phys. 17
1976
Earlier work this paper cites.
W. M. Tulczyjew, The Lagrange complex , Bull. Soc. Math. France 105
1977
Earlier work this paper cites.
A. M. Vinogradov, On algebro-geometric foundations of Lagrangian field theory , Soviet Math. Dokl. 18
1977
Earlier work this paper cites.
V. A. Belinskii and V. E. Zakharov, Integration of the Einstein equations by means of the inverse scattering problem technique and construction of exact soliton solutions , Soviet Phys. JETP 48
1978
Earlier work this paper cites.
B. K. Harrison, Bäcklund transformation for the Ernst equation of general relativity , Phys. Rev. Lett. 41
1978
Earlier work this paper cites.
F. Magri, A simple model of the integrable Hamiltonian equation , J. Math. Phys. 19
1978
Earlier work this paper cites.
D. Maison, Are the stationary, axially symmetric Einstein equations completely integrable? , Phys. Rev. Lett. 41
1978
Earlier work this paper cites.
J.-F. Pommaret, Systems of partial differential equations and Lie pseudogroups , Gordon and Breach, 1978
1978
Earlier work this paper cites.
A. M. Vinogradov, A spectral sequence associated with a nonlinear differential equation and algebro-geometric foundations of Lagrangian field theory with constraints , Soviet Math. Dokl. 19
1978
Earlier work this paper cites.
D. Maison, On the complete integrability of the stationary, axially symmetric Einstein equations , J. Math. Phys. 20
1979
Earlier work this paper cites.
Yu. I. Manin, Algebraic aspects of nonlinear differential equations , J. Soviet Math. 11
1979
Earlier work this paper cites.
F. Takens, A global version of the inverse problem of the calculus of variations , J. Differential Geom. 14
1979
Earlier work this paper cites.
R. K. Bullough and P. J. Caudrey (eds.), Solitons , Springer-Verlag, 1980
1980
Earlier work this paper cites.
B. A. Kupershmidt, Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalism , Geometric Methods in Mathematical Physics (G. Kaiser and J. E. Marsden, eds.), Lect. Notes Math., Springer-Verlag, 1980, pp. 162–218
1980
Earlier work this paper cites.
A. M. Vinogradov and I. S. Krasil ′
1980
Earlier work this paper cites.
I. M. Gel ′
1981
Earlier work this paper cites.
A. M. Vinogradov, Geometry of nonlinear differential equations , J. Soviet Math. 17
1981
Earlier work this paper cites.
L. V. Ovsiannikov, Group analysis of differential equations , Academic Press, 1982
1982
Earlier work this paper cites.
C. Rogers and W. F. Shadwick, Bäcklund transformations and their applications , Academic Press, 1982
1982
Earlier work this paper cites.
T. Tsujishita, On variation bicomplexes associated to differential equations , Osaka J. Math. 19
1982
Cited alongside, same era.
A. M. Astashov, Normal forms of Hamiltonian operators in field theory , Soviet Math. Dokl. 27
1983
Cited alongside, same era.
R. Dodd and A. Fordy, The prolongation structures of quasipolynomial flows , Proc. Roy. Soc. London Ser. A 385
1983
Cited alongside, same era.
S. I. Svinolupov, V. V. Sokolov, and R. I. Yamilov, On Bäcklund transformations for integrable evolution equations , Soviet Math. Dokl. 28
1983
Cited alongside, same era.
B. A. Dubrovin and S. P. Novikov, Poisson brackets of hydrodynamic type , Soviet Math. Dokl. 30
1984
Cited alongside, same era.
M. Marvan, Some local properties of Bäcklund transformations , Acta Appl. Math. 54
1998
Later among the works it cites.
A. M. Verbovetsky, Notes on the horizontal cohomology , Secondary Calculus and Cohomological Physics, Contemp. Math., vol. 219, Amer. Math. Soc., 1998, pp. 211–231, arXiv:math/9803115
1998
Later among the works it cites.
A. V. Bocharov, V. N. Chetverikov, S. V. Duzhin, N. G. Khor ′
1999
Later among the works it cites.
I. S. Krasil ′
2000
Later among the works it cites.
B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, Integrable systems. I , Dynamical Systems IV, Encyclopaedia of Mathematical Sciences, vol. 4, Springer-Verlag, 2 ed., 2001, pp. 173–280
2001
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1984
Cited alongside, same era.
A. M. Vinogradov, Category of nonlinear differential equations , Global Analysis—Studies and Applications I, Lect. Notes Math., vol. 1108, Springer-Verlag, 1984, pp. 77–102
1984
Cited alongside, same era.
A. M. Vinogradov, The 𝒞 \mathcal{C} -spectral sequence, Lagrangian formalism, and conservation laws. I
1984
Cited alongside, same era.
N. Ibragimov, Transformation groups applied to mathematical physics , D. Reidel, 1985
1985
Cited alongside, same era.
A. M. Astashov and A. M. Vinogradov, On the structure of Hamiltonian operators in field theory , J. Geom. Phys. 3
1986
Cited alongside, same era.
V. N. Chetverikov, On the structure of integrable 𝒞 \mathcal{C} -fields on infinitely prolonged equations , Soviet Math. Dokl. 33
1986
Cited alongside, same era.
I. S. Krasil ′
1986
Cited alongside, same era.
2001
Later among the works it cites.
E. Getzler, A Darboux theorem for Hamiltonian operators in the formal calculus of variations , Duke Math. J. 111
2002
Later among the works it cites.
S. Igonin and J. Krasil ′
2002
Later among the works it cites.
I. S. Krasil ′
2002
Later among the works it cites.
M. Marvan, On the horizontal gauge cohomology and nonremovability of the spectral parameter , Acta Appl. Math. 72
2002
Later among the works it cites.
P. J. Olver, J. A. Sanders, and J. P. Wang, Ghost symmetries , J. Nonlinear Math. Phys. 9
2002
Later among the works it cites.
C. Rogers and W. K. Schief, Bäcklund and Darboux transformations , Cambridge University Press, 2002
2002
Later among the works it cites.
L. A. Dickey, Soliton equations and Hamiltonian systems , 2nd ed., World Scientific, 2003
2003
Later among the works it cites.
S. Igonin, A. Verbovetsky, and R. Vitolo, Variational multivectors and brackets in the geometry of jet spaces , Symmetry in Nonlinear Mathematical Physics. Part 3, Institute of Mathematics of NAS of Ukraine, Kiev, 2003, pp. 1335–1342, URL http://www.imath.kiev.ua/~snmp2003/Proceedings/vitolo.pdf
2003
Later among the works it cites.
M. Marvan, Recursion operators for vacuum Einstein equations with symmetries , Symmetry in Nonlinear Mathematical Physics. Part 1, Institute of Mathematics of NAS of Ukraine, Kiev, 2003, pp. 179–183, URL http://www.imath.kiev.ua/~snmp2003/Proceedings/marvan.pdf
2003
Later among the works it cites.
P. Kersten, I. Krasil ′
2004
Later among the works it cites.
P. Kersten, I. Krasil ′
2004
Later among the works it cites.
P. Kersten, I. Krasil ′
2004
Later among the works it cites.
P. Kersten, I. Krasil ′
2004
Later among the works it cites.
A. Sergyeyev, Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: A new application for formal symmetries , Acta Appl. Math. 83
2004
Later among the works it cites.
P. Kersten, I. Krasil ′
2006
Later among the works it cites.
A. Kushner, V. Lychagin, and V. Rubtsov, Contact geometry and non-linear differential equations , Cambridge University Press, 2007
2007
Later among the works it cites.
A. M. Verbovetsky, V. A. Golovko, and I. S. Krasil ′
2007
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
B. Kruglikov and V. Lychagin, Geometry of differential equations , Handbook of Global Analysis (D. Krupka and D. J. Saunders, eds.), Elsevier, 2008, pp. 725–771, 1214
2008
Later among the works it cites.
B. A. Kupershmidt, KdV6: An integrable system , Phys. Lett. A 372
2008
Later among the works it cites.
2008
Later among the works it cites.
D. J. Saunders, Jet manifolds and natural bundles , Handbook of Global Analysis (D. Krupka and D. J. Saunders, eds.), Elsevier, 2008, pp. 1035–1068, 1216
2008
Later among the works it cites.
R. Vitolo, Variational sequences , Handbook of Global Analysis (D. Krupka and D. J. Saunders, eds.), Elsevier, 2008, pp. 1115–1163, 1217
2008
Later among the works it cites.
2009
Later among the works it cites.
H. Baran and M. Marvan, On integrability of Weingarten surfaces: A forgotten class , J. Phys. A 42
2009
Later among the works it cites.
2009
Later among the works it cites.
S. Igonin, Analogues of coverings and the fundamental group for the category of partial differential equations , URL http://www.math.uu.nl/people/igonin/preprints/cfg-2009.pdf
2009
Later among the works it cites.
2009
Later among the works it cites.
Mikhailov (ed.), Integrability , Lect. Notes Phys., vol. 767, Springer-Verlag, 2009
2009
Later among the works it cites.
G. W. Bluman, A. F. Cheviakov, and S. C. Anco, Applications of symmetry methods to partial differential equations , Springer-Verlag, 2010
2010
Closest in time.
P. H. M. Kersten, I. S. Krasil ′
2010
Closest in time.
2010
Closest in time.
W. M. Seiler, The formal theory of differential equations and its applications in computer algebra , Springer-Verlag, 2010
2010
Closest in time.
2010
Closest in time.
M. Marvan, On the spectral parameter problem , Acta Appl. Math. 109
2031
Closest in time.
V. G. Drinfel ′
2036
Closest in time.