(Benton and Platzman 1972; Zwillinger 1995, p. 417; Zwillinger 1997, p. 130). The so-called nonplanar Burgers equation is given by
(Sachdev and Nair 1987; Zwillinger 1997, p. 131).
The inviscid case is related to the Bateman equation. If
satisfies the Bateman equation and , then satisfies , an inviscid Burgers equation (Fairlie and Leznov
1999).
Benton, E. R. and Platzman, G. W. "A Table of Solutions of the One-Dimensional Burgers Equation." Quart. Appl. Math.30,
195-212, 1972.Fairlie, D. B. and Leznov, A. N. "The Complex
Bateman Equation." Lett. Math. Phys.49, 213-216, 1999. https://doi.org/10.1023/A:1007619823018.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.
satisfies the Bateman equation and 
, then 
satisfies 
, an inviscid Burgers equation (Fairlie and Leznov
1999).
