2024/03/25 by Hong, Younghun, Yang, Changhun · 1 citation
#35Q53 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.16648
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 by \citeSchneider1998 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.