The second-order ordinary
differential equation
 |
(1)
|
is called Liouville's equation (Goldstein and Braun 1973; Zwillinger 1997, p. 124),
as are the partial differential equations
 |
(2)
|
(Matsumo 1987; Zwillinger 1997, p. 133) and
 |
(3)
|
(Calogero and Degasperis 1982, p. 60; Zwillinger 1997, p. 133).
See also
Klein-Gordon Equation
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References
Calogero, F. and Degasperis, A. Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations.
New York: North-Holland, p. 60, 1982.Goldstein, M. E. and
Braun, W. H. Advanced
Methods for the Solution of Differential Equations. NASA SP-316. Washington,
DC: U.S. Government Printing Office, p. 98, 1973.Matsumo, Y. "Exact
Solution for the Nonlinear Klein-Gordon and Liouville Equations in Four-Dimensional
Euclidean Space." J. Math. Phys. 28, 2317-2322, 1987.Zwillinger,
D. Handbook
of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 124
and 133, 1997.Referenced on Wolfram|Alpha
Liouville's Equation
Cite this as:
Weisstein, Eric W. "Liouville's Equation."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LiouvillesEquation.html
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