Ah. Khater et al., 2 NEW CLASSES OF EXACT-SOLUTIONS FOR THE KDV EQUATION VIA BACKLUND-TRANSFORMATIONS, Chaos, solitons and fractals, 8(12), 1997, pp. 1901-1909
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.