Construction of solutions to the subcritical gKdV equations with a given asymptotical behavior

We consider the subcritical generalized Korteweg-de Vries equation u(t) + (u(xx) + u(4))(x) = 0, t, x is an element of R. Let R-j (t, x) = Q(cj)(x - x(j) - c(j)t) (j = 1,..., N) be N soliton solutions to this equation. Denote U(t) the KdV linear group, and let V be in an adequate weighted Sobolev space. We construct a solution u(t) to the generalized Korteweg-de Vries equation such that [GRAPHICS] (C) 2006 Elsevier Inc. All rights reserved.