For the Benjamin-Ono equation, the leading long-time term with x = O(t^{1/2}) is an explicit universal profile obtained from linearizing the self-similar profile equation, for rational initial data with generic reflection coefficient behavior at the origin.
A proof of the soliton resolution conjecture for the
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
fields
math.AP 6years
2026 6verdicts
UNVERDICTED 6representative citing papers
Establishes local well-posedness in H^s(T) for s ≥ 1/2 and global well-posedness under small L^2 norm for periodic INLS using gauge transform and CCM integrability, plus unconditional energy-space results and infinite-depth convergence.
Constructs a parametrized family of smooth finite-time blow-up solutions for the focusing Calogero-Sutherland derivative NLS on the circle with L2-mass in (1,2), explicit blow-up rate 1/(T-t)^{2s}, and describes the dynamics and instability.
An explicit formula for the Benjamin-Ono hierarchy is derived, allowing complete classification of traveling wave solutions and a geometric characterization of zero-dispersion limits.
The authors prove a spectral dichotomy for Benjamin-Ono solutions in L2 and use it to obtain asymptotic stability of multisolitons.
Explicit L^∞ asymptotic error formulas are established for the soliton resolution of the Benjamin-Ono equation in finite- and infinite-order multisoliton regimes.
citing papers explorer
-
The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality
For the Benjamin-Ono equation, the leading long-time term with x = O(t^{1/2}) is an explicit universal profile obtained from linearizing the self-similar profile equation, for rational initial data with generic reflection coefficient behavior at the origin.
-
Well-posedness for the periodic Intermediate nonlinear Schr\"{o}dinger equation
Establishes local well-posedness in H^s(T) for s ≥ 1/2 and global well-posedness under small L^2 norm for periodic INLS using gauge transform and CCM integrability, plus unconditional energy-space results and infinite-depth convergence.
-
Finite-time blow-up solutions for the Calogero--Sutherland derivative NLS
Constructs a parametrized family of smooth finite-time blow-up solutions for the focusing Calogero-Sutherland derivative NLS on the circle with L2-mass in (1,2), explicit blow-up rate 1/(T-t)^{2s}, and describes the dynamics and instability.
-
An Explicit Formula for the Benjamin-Ono Hierarchy with Applications to Traveling Waves and Zero-Dispersion Limits
An explicit formula for the Benjamin-Ono hierarchy is derived, allowing complete classification of traveling wave solutions and a geometric characterization of zero-dispersion limits.
-
Asymptotic stability of Benjamin--Ono multisolitons in $L^2(\mathbb R)$
The authors prove a spectral dichotomy for Benjamin-Ono solutions in L2 and use it to obtain asymptotic stability of multisolitons.
-
Soliton resolution conjecture for the Benjamin-Ono equation: Explicit $L^\infty$ asymptotic error formula
Explicit L^∞ asymptotic error formulas are established for the soliton resolution of the Benjamin-Ono equation in finite- and infinite-order multisoliton regimes.