On the Korteweg-de Vries limit for the Boussinesq equation

초록

The Korteweg-de Vries (KdV) equation is known as a universal equation describing various long waves in dispersive systems. In this article, we prove that in a certain scaling regime, a large class of rough solutions to the Boussinesq equation are approximated by the sums of two counter-propagating waves solving the KdV equations. It extends the earlier result [25] to slightly more regular than L2-solutions. Our proof is based on robust Fourier analysis methods developed for the low regularity theory of nonlinear dispersive equations. © 2024 Elsevier Inc.

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