  We generalize the nonlinear one-dimensional equation for a fluid layer
surface to any geometry and we introduce a new infinite order differential
equation for its traveling solitary waves solutions. This equation can be
written as a finite-difference expression, with a general solution that is a
power series expansion with coefficients satisfying a nonlinear recursion
relation. In the limit of long and shallow water, we recover the Korteweg-de
Vries equation together with its single-soliton solution.
