Generalized KdV Equation for Fluid Dynamics and Quantum Algebras
  We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution written as a power series expansion with coefficients satisfying a nonlinear recurrence relation. In the limit of long and shallow water (shallow channels) we reobtain the well known Korteweg-de-Vries equation together with its single-soliton solution. 
A. Ludu, R. A. Ionescu, W. Greiner (Frankfurt/Main University,   Germany)