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Gardner Equation

The partial differential equation

w_t-6(w+epsilon^2w^2)w_x+w_(xxx)=0,

which can also be rewritten

(w)_t+(-3w^2-2epsilon^2w^3+w_(xx))_x=0.

See also

Korteweg-de Vries Equation

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References

Miura, R. M.; Gardner, C. S.; and Kruskal, M. D. "Korteweg-de Vries Equation and Generalizations, II. Existence of Conservation Laws and Constants of Motion." J. Math. Phys. 9, 1204, 1968. Tabor, M. Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, p. 289, 1989.

Referenced on Wolfram|Alpha

Gardner Equation

Cite this as:

Weisstein, Eric W. "Gardner Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GardnerEquation.html

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