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Burgers' Equation

The partial differential equation

u_t+uu_x=nuu_(xx)

(Benton and Platzman 1972; Zwillinger 1995, p. 417; Zwillinger 1997, p. 130). The so-called nonplanar Burgers equation is given by

u_t+uu_x+(Ju)/(2t)=1/2deltau_xx

(Sachdev and Nair 1987; Zwillinger 1997, p. 131).

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References

Benton, E. R. and Platzman, G. W. "A Table of Solutions of the of the One-Dimensional Burgers Equation." Quart. Appl. Math. 30, 195-212, 1972.Sachdev, P. L. and Nair, K. R. C. "Generalized Burgers Equations and Euler-Painlevé Transcendents. II." J. Math. Phys. 28, 997-1004, 1987.Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 417, 1995.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 130, 1997.

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Burgers' Equation

Cite this as:

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

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