Abstract
In this paper, a new approach to Backlund transformations of nonlinear evolution equations is presented. The results obtained by this procedure are completely the same as that by Painleve truncating expansion.
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J. Weiss, M. Tabor and G. Carnevale, The Painleve property for partial differential equations,J. Math. Phys.,24, 3 (1983), 522.
G. Z. Tu, Backlund transformation and conservation law,Acta. Math. Appl. Sinica,4, 1 (1981), 63–68. (in Chinese)
Y. Cheng et al, Connections among symmetries, Backlund transformation and Painleve property,Acta. Math. Appl. Sinica,14, 2 (1991), 180–184. (in Chinese)
Y. B. Zeng, Recursion operator and Painleve property,Chin. Ann. Math.,12A, 1 (1991). 78–88. (in Chinese)
J. Weiss, The Painleve property and Backlund transformations for the sequence of Boussinesq equations.J. Math. Phys. 26, 2 (1985), 258–269.
C. Chou, Backlund transformations of solutions for different equations,Chinese Science Bulletin,32, 21 (1987), 1601–1605. (in Chinese)
M. J. Ablowitz and P. A. Clarkson,Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press (1991), 8–68, 359–420.
B. L. Guo,Nonlinear Evolution Equation, Shanghai Science Press (1995), 162–188. (in Chinese)
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Project supported by the National Natural Science Foundation of China and the Center of Mathematics Mechanization
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Engui, F., Hongqing, Z. A new approach to backlund transformations of nonlinear evolution equations. Appl Math Mech 19, 645–650 (1998). https://doi.org/10.1007/BF02452372
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DOI: https://doi.org/10.1007/BF02452372