A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.
Bäcklund Transformation
See also
Inverse Scattering Method, SolitonReferences
Anderson, R. L. and Ibragimov, N. H. Lie-Bäcklund Transformation in Applications. Philadelphia, PA: SIAM, 1979.Dodd, R. K.; Eilbeck, J. C.; and Morris, H. C. Solitons and Nonlinear Equations. London: Academic Press, 1984.Infeld, E. and Rowlands, G. "Bäcklund Transformations." §7.5 in Nonlinear Waves, Solitons, and Chaos, 2nd ed. Cambridge, England: Cambridge University Press, pp. 175-177, 2000.Lamb, G. L. Jr. Elements of Soliton Theory. New York: Wiley, 1980.Miura, R. M. (Ed.). Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications. New York: Springer-Verlag, 1974.Olver, P. J. Applications of Lie Groups to Differential Equations. New York: Springer-Verlag, 1986.Rogers, C. and Shadwick, W. F. Bäcklund Transformations and Their Applications. New York: Academic Press, 1982.Whitham, G. B. Linear and Nonlinear Waves. New York: Wiley, pp. 609-611, 1974.Zwillinger, D. "Bäcklund Transformations." §87 in Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 321-324, 1997.Referenced on Wolfram|Alpha
Bäcklund TransformationCite this as:
Weisstein, Eric W. "Bäcklund Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BaecklundTransformation.html