A Lagrangian form of the KdV equation (LKdV) is given which governs the evolution of nonlinear shallow water waves. Wave motion described by this equation in the context of the inverse scattering transform (IST) is discussed. For a single soliton it is shown that LKdV allows for an orthogonal decomposition of the particle motion into a kink (tanh) soliton in the horizontal and a pulse (sech2) soliton in the vertical. Generalizations to the orthogonal decomposition ofN‐soliton motion and to motion with periodic boundary conditions are also discussed. Implications of this approach on experimental measurements and on other integrable (soliton) systems are briefly explored.