2019/06/04 by Felipe Linares, Linares, Felipe, Argenis J. Méndez +3
Mathematics · Physics and Astronomy · #35B40 #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1906.01473
openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for any uniformly bounded in time H1\∩ L1 solution of the\ndispersive generalized Benjamin-Ono equation, the limit infimum, as time t\ngoes to infinity, converges to zero locally in an increasing-in-time region of\nspace of order t/\log t. This result is in accordance with the one\nestablished by Mu ~noz and Ponce citeMP1 for solutions of the Benjamin-Ono\nequation. Similar to solutions of the Benjamin-Ono equation, for a solution of\nthe dispersive generalized Benjamin-Ono equation, with a mild L1-norm growth\nin time, its limit infimum must converge to zero, as time goes to infinity,\nlocally in an increasing on time region of space of order depending on the rate\nof growth of its L1-norm. As a consequence, the existence of breathers or\nany other solution for the dispersive generalized Benjamin-Ono equation moving\nwith a speed "slower" than a soliton is discarded. In our analysis the use of\ncommutators expansions is essential.\n