On uniqueness properties of solutions of the k-generalized KdV equations

In this paper we study uniqueness properties of solutions of the so-called k-generalized Korteweg– de Vries equations. Our goal is to obtain sufficient conditions on the behavior of the difference u1 − u2 of two solutions u1,u2 of (1.1) at two different times t0 = 0 and t1 = 1 which guarantee that u1 ≡ u2. © 2006 Elsevier Inc. All rights reserved