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On the basis of the Lagrangian method a nonlinear wave theory is developed to obtain the Korteweg-de Vries equation for the incompressible, one-dimensional, weak-nonlinear, and dispersive motion of fluid in an infinitely long circular cylinder (with thin walls of elastic rings). This equation has first been obtained by Lamb [1] via the reductive Taniuti-Wei's method [2].

The Korteweg-de Vries Equation for Wave Propagation in an Infinitely Long Thin Walled Circular Cylinder Obtained via the Lagrangian Method