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Volumn 83, Issue 1-2 SPEC. ISS., 2004, Pages 95-109

Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: A new application for formal symmetries

Author keywords

Evolution equations; Formal symmetry; Generalized symmetries; Integrability; Recursion operator

Indexed keywords

ALGEBRA; FUNCTIONS; HAMILTONIANS; POISSON EQUATION; THEOREM PROVING;

EID: 3242760654     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ACAP.0000035591.77558.2c     Document Type: Article
Times cited : (4)

References (29)
  • 1
    • 3242759616 scopus 로고
    • Lie-algebraic approach to nonlocal symmetries of integrable systems
    • Adler, V. E.: Lie-algebraic approach to nonlocal symmetries of integrable systems, Theoret. Math. Phys. 89 (1992), 1239-1248.
    • (1992) Theoret. Math. Phys. , vol.89 , pp. 1239-1248
    • Adler, V.E.1
  • 3
    • 0009147712 scopus 로고    scopus 로고
    • On the construction of recursion operator and algebra of symmetries for field and lattice systems
    • Błaszak, M.: On the construction of recursion operator and algebra of symmetries for field and lattice systems, Rep. Math. Phys. 48 (2000), 27-38.
    • (2000) Rep. Math. Phys. , vol.48 , pp. 27-38
    • Błaszak, M.1
  • 4
    • 0002641090 scopus 로고
    • Reduction technique for matrix nonlinear evolution equations solvable by the spectral transform
    • Calogero, F. and Degasperis, A.: Reduction technique for matrix nonlinear evolution equations solvable by the spectral transform, J. Math. Phys. 22 (1981), 23-31.
    • (1981) J. Math. Phys. , vol.22 , pp. 23-31
    • Calogero, F.1    Degasperis, A.2
  • 5
    • 0009957990 scopus 로고
    • Symmetries and a hierarchy of the general KdV equation
    • Chou, T.: Symmetries and a hierarchy of the general KdV equation, J. Phys. A: Math. Gen. 20 (1987), 359-366.
    • (1987) J. Phys. A: Math. Gen. , vol.20 , pp. 359-366
    • Chou, T.1
  • 6
    • 34250120087 scopus 로고
    • Lie algebras and equations of Korteweg-de Vries type
    • Drinfeld, V. G. and Sokolov, V. V.: Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math. 30 (1985), 1975-2036.
    • (1985) J. Soviet Math. , vol.30 , pp. 1975-2036
    • Drinfeld, V.G.1    Sokolov, V.V.2
  • 8
    • 36749119273 scopus 로고
    • A symmetry approach to exactly solvable evolution equations
    • Fokas, A. S.: A symmetry approach to exactly solvable evolution equations, J. Math. Phys. 21 (1980), 1318-1325.
    • (1980) J. Math. Phys. , vol.21 , pp. 1318-1325
    • Fokas, A.S.1
  • 9
    • 0001218076 scopus 로고
    • The Lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems
    • Fuchssteiner, B.: The Lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems, Progr. Theor. Phys. 68 (1982), 1082-1104.
    • (1982) Progr. Theor. Phys. , vol.68 , pp. 1082-1104
    • Fuchssteiner, B.1
  • 10
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • Fuchssteiner, B. and Fokas, A. S.: Symplectic structures, their Bäcklund transformations and hereditary symmetries, Physica D 4 (1981/82), 47-66.
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 11
    • 0033249099 scopus 로고    scopus 로고
    • On construction of recursion operators from Lax representation
    • Gürses, M., Karasu, A. and Sokolov, V. V.: On construction of recursion operators from Lax representation, J. Math. Phys. 40 (1999), 6473-6490.
    • (1999) J. Math. Phys. , vol.40 , pp. 6473-6490
    • Gürses, M.1    Karasu, A.2    Sokolov, V.V.3
  • 12
    • 0009955869 scopus 로고
    • Recursion operators and non-local symmetries
    • Guthrie, G. A.: Recursion operators and non-local symmetries, Proc. Roy. Soc. London Ser. A 446 (1926) (1994), 107-114.
    • (1994) Proc. Roy. Soc. London Ser. A , vol.446 , Issue.1926 , pp. 107-114
    • Guthrie, G.A.1
  • 13
    • 3242759848 scopus 로고    scopus 로고
    • A strange recursion operator for a new integrable system of coupled Korteweg-de Vries equations
    • Karasu (Kalkanli), A., Karasu, A. and Sakovich, S. Yu.: A strange recursion operator for a new integrable system of coupled Korteweg-de Vries equations, Acta Appl. Math. 83(1-2) (2004), 85-94.
    • (2004) Acta Appl. Math. , vol.83 , Issue.1-2 , pp. 85-94
    • Karasu, A.1    Karasu, A.2    Sakovich, S.Yu.3
  • 14
    • 0042316954 scopus 로고
    • On the nonhereditary recursion operator and the constraint on the potential associated with the Giachetti-Johnson equation and its gauge equivalent Yang equation
    • Li, Y. S. and Zeng, Y. B.: On the nonhereditary recursion operator and the constraint on the potential associated with the Giachetti-Johnson equation and its gauge equivalent Yang equation, J. Phys. A: Math. Gen. 23 (1990), 721-733.
    • (1990) J. Phys. A: Math. Gen. , vol.23 , pp. 721-733
    • Li, Y.S.1    Zeng, Y.B.2
  • 15
    • 0043001185 scopus 로고
    • Another look on recursion operator
    • J. Janyška, I. Kolář and J. Slovák (eds), (Brno), Masaryk University, Brno, 1996
    • Marvan, M.: Another look on recursion operator, In: J. Janyška, I. Kolář and J. Slovák (eds), Differential Geometry and Applications (Brno, 1995), Masaryk University, Brno, 1996, pp. 393-402, URL http://www.emis.de/proceedings.
    • (1995) Differential Geometry and Applications , pp. 393-402
    • Marvan, M.1
  • 16
    • 33947180234 scopus 로고
    • The symmetry approach to classification of nonlinear equations. Complete lists of integrable systems
    • Mikhailov, A. V., Shabat, A. B. and Yamilov, R. I.: The symmetry approach to classification of nonlinear equations. Complete lists of integrable systems, Russian Math. Surveys 42(4) (1987), 1-63.
    • (1987) Russian Math. Surveys , vol.42 , Issue.4 , pp. 1-63
    • Mikhailov, A.V.1    Shabat, A.B.2    Yamilov, R.I.3
  • 17
    • 0002318306 scopus 로고
    • The symmetry approach to classification of integrable equations
    • V. E. Zakharov (ed.), Springer, New York
    • Mikhailov, A. V., Shabat, A. B. and Sokolov, V. V.: The symmetry approach to classification of integrable equations, In: V. E. Zakharov (ed.), What is Integrability?, Springer, New York, 1991, pp. 115-184.
    • (1991) What Is Integrability? , pp. 115-184
    • Mikhailov, A.V.1    Shabat, A.B.2    Sokolov, V.V.3
  • 18
    • 0032493605 scopus 로고    scopus 로고
    • Towards classification of (2 + 1)-dimensional integrable equations. Integrability conditions. I
    • Mikhailov, A. V. and Yamilov, R. I.: Towards classification of (2 + 1)-dimensional integrable equations. Integrability conditions. I, J. Phys. A: Math. Gen. 31 (1998), 6707-6715.
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 6707-6715
    • Mikhailov, A.V.1    Yamilov, R.I.2
  • 19
    • 36749108571 scopus 로고
    • Evolution equations possessing infinitely many symmetries
    • Olver, P. J.: Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), 1212-1215.
    • (1977) J. Math. Phys. , vol.18 , pp. 1212-1215
    • Olver, P.J.1
  • 20
    • 0040875591 scopus 로고
    • Bi-Hamiltonian systems
    • (Dundee), Longman, Harlow, 1987
    • Olver, P. J.: Bi-Hamiltonian systems, In: Ordinary and Partial Differential Equations (Dundee, 1986), Longman, Harlow, 1987, pp. 176-193.
    • (1986) Ordinary and Partial Differential Equations , pp. 176-193
    • Olver, P.J.1
  • 22
    • 0035423333 scopus 로고    scopus 로고
    • Integrable systems and their recursion operators
    • Sanders, J. A. and Wang, J. P.: Integrable systems and their recursion operators, Nonlinear Anal. 47 (2001), 5213-5240.
    • (2001) Nonlinear Anal. , vol.47 , pp. 5213-5240
    • Sanders, J.A.1    Wang, J.P.2
  • 23
    • 0040755058 scopus 로고    scopus 로고
    • On recursion operators
    • Sanders, J. A. and Wang, J. P.: On recursion operators, Physica D 149 (2001), 1-10.
    • (2001) Physica D , vol.149 , pp. 1-10
    • Sanders, J.A.1    Wang, J.P.2
  • 24
    • 0039359643 scopus 로고
    • A coupled KdV equation is one case of the four-reduction of the KP hierarchy
    • Satsuma, J. and Hirota, R.: A coupled KdV equation is one case of the four-reduction of the KP hierarchy, J. Phys. Soc. Japan 51(10) (1982), 3390-3397.
    • (1982) J. Phys. Soc. Japan , vol.51 , Issue.10 , pp. 3390-3397
    • Satsuma, J.1    Hirota, R.2
  • 25
    • 0009907846 scopus 로고    scopus 로고
    • On recursion operators and nonlocal symmetries of evolution equations
    • D. Krupka (ed.), Silesian University in Opava, arXiv:nlin.SI/0012011
    • Sergyeyev, A.: On recursion operators and nonlocal symmetries of evolution equations, In: D. Krupka (ed.), Proc. Sem. Diff. Geom., Silesian University in Opava, 2000, pp. 159-173, arXiv:nlin.SI/0012011.
    • (2000) Proc. Sem. Diff. Geom. , pp. 159-173
    • Sergyeyev, A.1
  • 26
    • 0036986385 scopus 로고    scopus 로고
    • On sufficient conditions of locality for hierarchies of symmetries of evolution systems
    • Sergyeyev, A.: On sufficient conditions of locality for hierarchies of symmetries of evolution systems, Rep. Math. Phys. 50 (2002), 307-314.
    • (2002) Rep. Math. Phys. , vol.50 , pp. 307-314
    • Sergyeyev, A.1
  • 27
    • 3242801063 scopus 로고    scopus 로고
    • On homogeneous symmetries for evolution systems with constraints
    • Sergyeyev, A.: On homogeneous symmetries for evolution systems with constraints, Rend. Circ. Mat. Palermo Ser. II Suppl. 69 (2002), 219-231.
    • (2002) Rend. Circ. Mat. Palermo Ser. II Suppl. , vol.69 , pp. 219-231
    • Sergyeyev, A.1
  • 28
    • 0000438720 scopus 로고
    • Symmetries of evolution equations
    • Sokolov, V. V.: Symmetries of evolution equations, Russian Math. Surveys 43(5) (1988), 165-204.
    • (1988) Russian Math. Surveys , vol.43 , Issue.5 , pp. 165-204
    • Sokolov, V.V.1
  • 29
    • 84960389894 scopus 로고    scopus 로고
    • A list of 1 + 1 dimensional integrable equations and their properties
    • Wang, J. P.: A list of 1 + 1 dimensional integrable equations and their properties, J. Nonlinear Math. Phys. 9(Suppl. 1) (2002), 213-233.
    • (2002) J. Nonlinear Math. Phys. , vol.9 , Issue.SUPPL. 1 , pp. 213-233
    • Wang, J.P.1


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