Johnson's Equation

The Partial Differential Equation

$${\partial\over\partial x}\left({u_t+uu_x+{\textstyle{1\over 2}}u_{xxx}+{u\over 2t}}\right)+{3\alpha^2\over 2t^2} u_{yy}=0$$

which arises in the study of water waves.

References

Infeld, E. and Rowlands, G. Nonlinear Waves, Solitons, and Chaos. Cambridge, England: Cambridge University Press, p. 223, 1990.