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

We consider the subcritical generalized Korteweg–de Vries equation ut + uxx +u4 x = 0, t,x∈ R. Let Rj (t, x) =Qcj (x − xj − cj 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 lim t→∞ u(t) − U(t)V − N j=1 Rj (t) H1 = 0. © 2006 Elsevier Inc. All rights reserved.