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Benney Equation

The Benney equation in 1+1 dimensions is the nonlinear partial differential equation

(partialpsi(x,t))/(partialt)+psi(x,t)(partialpsi(x,t))/(partialx)+(partial^2phi(x,t))/(partialx^2) +epsilon(partial^3psi(x,t))/(partialx^3)+(partial^4psi(x,t))/(partialx^4)=0.

See also

Partial Differential Equation

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References

Konno, H. and Lomdahl, P. S. "The Birth-Death Stochastic Processes of 'Solitons' in the 1D Benney Equation." J. Phys. Soc. Japan 69, 1629-1641, 2000.Pego, R. L.; Quintero, J. R. "Two-Dimensional Solitary Waves for a Benney-Luke Equation." Physica D 132, 476-496, 1999.Rosenau, P.; Oron, A.; and Hyman, J. M. "Bounded and Unbounded Patterns of the Benney Equation." Phys. Fluids A 4, 1102-1104, 1992.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, pp. 14-16, 2004. http://www.mathematicaguidebooks.org/.

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Benney Equation

Cite this as:

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

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