Bicomplexes and Bäcklund transformations

Journal of Physics A: Mathematical and General

Volumn 34, Issue 43, 2001, Pages 9163-9194

  Dimakis, A ^a   Muller Hoissen F ^b  

^a UNIVERSITY OF THE AEGEAN   (Greece)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035798525     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/43/306     Document Type: Article

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79. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
80. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
81. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
82. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
83. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
84. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
85. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
86. Ibragimov N 1981 Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie-Bäcklund infinie C. R. Acad. Sci., Paris 293 657-60 Weiss J 1983 The Painlevé property for partial differential equations: II. Bäcklund transformation, Lax pairs, and the Schwarzian derivative J. Math. Phys. 24 1405-13 Weiss J 1986 Bäcklund transformations and the Painleve property J. Math. Phys. 27 1293-305 Levi D, Ragnisco O and Sym A 1984 The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons Phys. Lett. A 100 7-10 Kawamoto S 1985 An exact transformation from the Harry Dym equation to the modified KdV equation J. Phys. Soc. Japan 54 2055-6 Clarkson P A, Fokas A S and Ablowitz M J 1989 Hodograph transformations of linearizable partial differential equations SIAM J. Appl. Math. 49 1188-209 Fuchssteiner B and Carillo S 1989 Soliton structure versus singularity analysis: third-order completely integrable nonlinear differential equations in 1 + 1 dimensions Physica A 154 467-510 Guo B-Y and Rogers C 1989 On Harry Dym equation and its solution Sci. China A 32 283-95 Gesztesy F and Unterkofler K 1992 Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations Rep. Math. Phys. 31 113-37
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88. Krichever I M and Novikov S P 1980 Holomorphic bundles over algebraic curves and non-linear equations Russ. Math. Surv. 35 53-79 Guil F and Mañas M 1991 Loop algebras and the Krichever-Novikov equation Phys. Lett. A 153 90-4
89. Krasil'shchik I S, Lychagin V V and Vinogradov AM 1986 Geometry of Jet Spaces and Nonlinear Partial Differential Equations (New York: Gordon and Breach) Krasil'shchik I S and Vinogradov A M 1989 Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations Acta Appl. Math. 15 161-209
90. Krasil'shchik I S, Lychagin V V and Vinogradov AM 1986 Geometry of Jet Spaces and Nonlinear Partial Differential Equations (New York: Gordon and Breach) Krasil'shchik I S and Vinogradov A M 1989 Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations Acta Appl. Math. 15 161-209