2 NEW CLASSES OF EXACT-SOLUTIONS FOR THE KDV EQUATION VIA BACKLUND-TRANSFORMATIONS

The Korteweg-de Vries equation which includes nonlinear and dispersive terms quadratic in the wave amplitude is considered. The exact soluti ons can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the a ssociated AKNS system: that is. a linear eigenvalue problem in the for m of a system of first order partial differential equations. The metho d of characteristics is used and Backlund transformations (BTs) are em ployed to gent rate two new solutions from the old one. (C) 1997 Elsev ier Science Ltd.