Scattering for the Quartic Generalized Benjamin-Bona-Mahony Equation

Autor:	Morgan, A. George
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35Q35 76B15
Druh dokumentu:	Working Paper
Popis:	The generalized Benjamin-Bona-Mahony equation (gBBM) is a model for nonlinear dispersive waves which, in the long-wave limit, is approximately equivalent to the generalized Korteweg-de Vries equation (gKdV). While the long-time behaviour of small solutions to gKdV is well-understood, the corresponding theory for gBBM has progressed little since the 1990s. Using a space-time resonance approach, I establish linear dispersive decay and scattering for small solutions to the quartic-nonlinear gBBM. To my knowledge, this result provides the first global-in-time pointwise estimates on small solutions to gBBM with a nonlinear power less than or equal to five. Owing to nonzero inflection points in the linearized gBBM dispersion relation, there exist isolated space-time resonances without null structure, but in the course of the proof I show these resonances do not obstruct scattering. Comment: 63 pages, 15 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.09605 Zobrazit plný text záznamu View this record from Arxiv