Year: 2026
Type: preprint
Abstract: We consider the quintic generalized Benjamin-Bona-Mahony equation $$ u_t-u_{xxt} + \partial_x\big(u + u^{5}\big)= 0,\qquad (t,x)\in \mathbb{R}_+ \times \mathbb{R}. $$ Using the space-time resonance method, we prove that sufficiently small and smooth solutions scatter to the linear flow. While the higher nonlinearity simplifies the treatment of nonresonant interactions compared to the quartic model in \cite{Morgan}, resonance analysis is more intricate. The resonance analysis occurs in a higher-dimensional geometric setting, and certain null or vanishing conditions present in the quartic case fail at specific resonance points. As a result, refined computations and precise estimates near the resonant set are required to close the bootstrap argument.
Source: arXiv (Cornell University)
Authors: Chen, Gong, Zhang, Yingmo
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7133305316
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