text: While the Boussinesq equations allow for waves traveling simultaneously in opposing directions, it is often advantageous to only consider waves traveling in one direction. Under small additional assumptions, the Boussinesq equations reduce to:
  *the Korteweg–de Vries equation for wave propagation in one horizontal dimension,
  *the Kadomtsev–Petviashvili equation for (near uni-directional) wave propagation in two horizontal dimensions,
  *the nonlinear Schrödinger equation (NLS equation) for the complex-valued amplitude of narrowband waves (slowly modulated waves).
  Besides solitary wave solutions, the Korteweg–de Vries equation also has periodic and exact solutions, called cnoidal waves. These are approximate solutions of the Boussinesq equation.