PreprintCC BY 4.0HAL
The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality
Abstract
We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit t → +∞ with x = O(t^(1/2) ). We show that the rate of decay exceeds that of self-similar solutions and obtain an explicit universal profile for the decaying solution, relating it to the linearization of the profile equation for self-similar solutions. The proof assumes a class of rational initial data u_0 in L^2 (R) ∩ L^1 (R) that exhibit generic behavior of the reflection coefficient at the origin.
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BibTeX
@misc{gassot2026benjaminono,
title = {{The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality}},
author = {Louise Gassot and Patrick Gérard and Peter D. Miller},
howpublished = {HAL},
year = {2026},
month = jun,
eprint = {2606.02989},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05765501v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality
AU - Louise Gassot
AU - Patrick Gérard
AU - Peter D. Miller
PY - 2026
DA - 2026/06/02
PB - HAL
UR - https://hal.science/hal-05765501v1
AB - We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit t → +∞ with x = O(t^(1/2) ). We show that the rate of decay exceeds that of self-similar solutions and obtain an explicit universal profile for the decaying solution, relating it to the linearization of the profile equation for self-similar solutions. The proof assumes a class of rational initial data u_0 in L^2 (R) ∩ L^1 (R) that exhibit generic behavior of the reflection coefficient at the origin.
ER -