Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/recursion-operator-for-the-intrinsic-generalized-sine-gordon-equation-0b28ClsdQ3
References (40)
-
J. Douglas (1939)
Solution of the Inverse Problem of the Calculus of Variations.Proceedings of the National Academy of Sciences of the United States of America, 25 12
-
J. Barbosa, W. Ferreira, K. Tenenblat (1996)
Submanifolds of constant sectional curvature in Pseudo-Riemannian manifoldsAnnals of Global Analysis and Geometry, 14
-
D. Ferus, F. Pedit (1995)
Isometric immersions of space forms and soliton theoryMathematische Annalen, 305
-
S. Kumei (1975)
Invariance transformations, invariance group transformations, and invariance groups of the sine‐Gordon equationsJournal of Mathematical Physics, 16
-
M. Marvan (1998)
Some Local Properties of Bäcklund TransformationsActa Applicandae Mathematica, 54
-
V. Zakharov, B. Konopelchenko (1984)
On the theory of recursion operatorCommunications in Mathematical Physics, 94
-
M. Marvan (2002)
Scalar second-order evolution equations possessing an irreducible sl 2-valued zero-curvature representationJ. Phys. A: Math. Gen., 35
-
I. Krasilshchik, Alexandre Vinogradov (1984)
Nonlocal symmetries and the theory of coverings: An addendum to A. M. vinogradov's ‘local symmetries and conservation laws”Acta Applicandae Mathematica, 2
-
Z. fifdul (2007)
A HIGHER DIMENSION GENERALIZATION OF THE SINE-GORDON EQUATION AND ITS BÀCKLUND TRANSFORMATION -
(1984)
Vinogradov,Nonlocalsym m etriesand the theory of coverings: An addendum to A.M -
N. G. Khor’kova (1988)
Conservation laws and nonlocal symmetriesMat. Zametki, 44
-
(1988)
Khor'kova, Zakony sokhraneniya i nelokal'nye simmetrii -
Zixiang Zhou (1998)
Darboux transformations for the twisted so(p, q) system and local isometric immersion of space formsInverse Problems, 14
-
W. Ferreira (1995)
On metrics of constant sectional curvatureMat. Contemp., 9
-
M. Marvan, Artur Sergyeyev (2002)
Recursion operator for the stationary Nizhnik?Veselov?Novikov equationJournal of Physics A, 36
-
P. Campos, K. Tenenblat (1994)
Backlund transformations for a class of systems of differential equationsGeometric & Functional Analysis GAFA, 4
-
C. Terng (1980)
A Higher Dimension Generalization of the Sine-Gordon Equation and its Soliton TheoryAnnals of Mathematics, 111
-
A. Bocharov, I. Krasilʹshchik, A. Vinogradov (1999)
Symmetries and conservation laws for differential equations of mathematical physics -
G. Guthrie (1994)
Recursion operators and non-local symmetriesProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 446
-
P. Olver (1977)
Evolution equations possessing infinitely many symmetriesJournal of Mathematical Physics, 18
-
M. Marvan, A. Sergyeyev (2003)
Recursion operator for the Nizhnik-Veselov-Novikov equationJ. Phys. A: Math. Gen., 36
-
K. Tenenblat (1992)
A note on solutions for the intrinsic generalized wave and sine-Gordon equationsJournal of Mathematical Analysis and Applications, 166
-
M. Marvan (1987)
Differential Geometry and Applications -
M. Boiti, J. Leon, F. Pempinelli (1988)
Canonical and Noncanonical Recursion Operators in MultidimensionsStudies in Applied Mathematics, 78
-
K. Tenenblat, P. Winternitz (1993)
On the symmetry groups of the intrinsic generalized wave and sine–Gordon equationsJournal of Mathematical Physics, 34
-
A. Fokas, P Santini (1988)
Recursion operators and bi-Hamiltonian structures in multidimensions. ICommunications in Mathematical Physics, 115
-
(2003)
Sergyeyev, Recursion operator for the Nizhnik{Veselov{Novikov equation,J.Phys.A:M ath.Gen.36 (2003)L87{L92 -
N. Khor’kova (1988)
Conservation laws and nonlocal symmetriesMathematical notes of the Academy of Sciences of the USSR, 44
-
(1977)
On immersions of regions of the n-dimensional Lobachevsky space into (2n − 1)-dimensional Euclidean space -
J. Douglas (1941)
Solution of the inverse problem of the calculus of variationsTrans. Amer. Math. Soc., 50
-
I. Krasil’shchik, Alexandre Vinogradov (1989)
Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformationsActa Applicandae Mathematica, 15
-
C. Terng (1997)
Soliton equations and differential geometryJournal of Differential Geometry, 45
-
(1995)
arvan, Another look on recursion operators, in: Differential Geom etry and Applications -
M. Marvan (1998)
Some local properties of Bäcklund relationsActa Appl. Math., 54
-
H. Baran, M. Marvan (2008)
A conjecture concerning nonlocal terms of recursion operatorsJournal of Mathematical Sciences, 151
-
J. Cieśliński, Yu. Aminov (2001)
A geometric interpretation of the spectral problem for the generalized sine-Gordon systemJournal of Physics A: Mathematical and General, 34
-
C. Gu, He-sheng Hu (1993)
Explicit solutions to the intrinsic generalization for the wave and sine-Gordon equationsLetters in Mathematical Physics, 29
-
M. Marvan (2002)
Scalar second-order evolution equations possessing an irreducible sl2-valued zero-curvature representationJournal of Physics A, 35
-
Al Young (1975)
Providence, Rhode IslandThe Iowa Review, 6
-
Artur Sergyeyev (2004)
Why nonlocal recursion operators produce local symmetries: new results and applicationsJournal of Physics A, 38
- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by Springer Science+Business Media, Inc.
- Subject
- Mathematics; Mathematics, general
- ISSN
- 1072-3374
- eISSN
- 1573-8795
- DOI
- 10.1007/s10958-008-9024-4
- Publisher site
- See Article on Publisher Site
Abstract
We find the inverse and direct recursion operator for the intrinsic generalized sine-Gordon equation in any number n > 2 of independent variables. Among the flows generated by the direct operator we identify a higher-dimensional analogue of the pmKdV equation.
Journal
Journal of Mathematical Sciences – Springer Journals
Published: Jul 8, 2008