AN ALGEBRAIC-METHOD FOR SOLVING THE KDV EQUATION (II) - 3-PARAMETER AND 4-PARAMETER SOLUTION FAMILY

The three-parameter and four-parameter solution family of the KdV equa tion are given; The comparison of our expressions with the known resul ts which were obtained by means of the inverse scattering transformati on (IST) or Backlund transformation is discussed in detail. We find th at the known result obtained by the IST approach is the special case o f our expressions and under some proper transformations, the expressio ns given here become the result obtained by Backlund transformation. I t is emphasized that the properties of these multiple-parameter soluti on families should be studied from algebraic-geometry approach. (C) 19 98 Elsevier Science Ltd. All rights reserved.