Bilinearization of Nonlinear Evolution Equations. III. Bäcklund Transformations of Higher-Order Korteweg-de Vries Equations

Abstract

The Bäcklund transformations of the higher-order Korteweg-de Vries (KdV) equations are derived on the basis of the bilinear transformation method. It is shown that these transformations are closely related to the quantities obtained from the functional derivative of conserved quantities of the modified KdV equation. The inverse scattering transforms of the higher-order KdV equations are also presented.