We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non dispersion.

中文翻译：

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广义 Korteweg-de Vries 方程的非色散解通常是多孤子

我们考虑广义 Korteweg-de Vries 方程 (gKdV) 的解，它在某种意义上是非色散的，并且仍然接近多孤子。我们表明这些解决方案必然是纯多孤子。特别是对于 Korteweg-de Vries 方程 (KdV) 和修正的 Korteweg-de Vries 方程 (mKdV)，我们在非色散方面获得了多孤子和多呼吸器的表征。