ON THE SUPPORT OF SOLUTIONS TO THE GENERALIZED KDV EQUATION

ABSTRACT. – It is shown that if u is a solution of the initial value problem for the generalized Korteweg–de Vries equation such that there exists b ∈ R with suppu(·, tj) ⊆ (b,∞) (or (−∞, b)), for j = 1,2 (t1 = t2), then u ≡ 0. 2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: Primary 35Q53; secondary 35G25; 35D9