On the support of solutions to the generalized KdV equation. (English) Zbl 1001.35106

Summary: It is shown that if \(u\) is a solution of the initial value problem for the generalized Korteweg-de Vries equation \[ \partial_tu+\partial^3_xu+u^k\partial_x u=0,\quad (x,t)\in\mathbb{R}\times (t_1,t_2),\quad k\in\mathbb{Z}^+, \] such that there exists \(b\in\mathbb{R}\) with \(\text{supp} u(\cdot,t_j)\subseteq (b,\infty)\) (or \((-\infty,b))\), for \(j=1,2\) \((t_1\neq t_2)\), then \(u\equiv 0\).


35Q53 KdV equations (Korteweg-de Vries equations)
35G25 Initial value problems for nonlinear higher-order PDEs
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