[HTML][HTML] A view of the peakon world through the lens of approximation theory

H Lundmark, J Szmigielski - Physica D: Nonlinear Phenomena, 2022 - Elsevier
Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

Reducible KAM tori for the Degasperis–Procesi equation

R Feola, F Giuliani, M Procesi - Communications in mathematical physics, 2020 - Springer
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian
perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall …

Quasi-periodic traveling waves on an infinitely deep fluid under gravity

R Feola, F Giuliani - arXiv preprint arXiv:2005.08280, 2020 - arxiv.org
We consider the gravity water waves system with a periodic one-dimensional interface in
infinite depth and we establish the existence and the linear stability of small amplitude, quasi …

[图书][B] Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity

R Feola, F Giuliani - 2024 - books.google.com
We consider the gravity water waves system with a periodic one-dimensional interface in
infinite depth and we establish the existence and the linear stability of small amplitude, quasi …

[HTML][HTML] A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation

H Cong, L Mi, P Wang - Journal of Differential Equations, 2020 - Elsevier
It is proved a Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation
in a Gevrey space. More precisely, we prove that if the norm of initial datum is equal to ε/2 …

Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation

R Feola, F Giuliani, M Procesi - arXiv preprint arXiv:1806.06604, 2018 - arxiv.org
We prove reducibility of a class of quasi-periodically forced linear equations of the
form\[\partial_tu-\partial_x\circ (1+ a (\omega t, x)) u+\mathcal {Q}(\omega t) u= 0,\quad …

Long time stability result for 1-dimensional nonlinear Schrödinger equation

Q Chen, H Cong, L Meng, X Wu - Journal of Differential Equations, 2022 - Elsevier
Long time stability result for 1-dimensional nonlinear Schrödinger equation - ScienceDirect
Skip to main contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View …

Super-exponential stability estimate for the nonlinear Schrödinger equation

H Cong, L Mi, Y Shi - Journal of Functional Analysis, 2022 - Elsevier
In this paper, we study the long-time stability of solutions for the 1-dimensional nonlinear
Schrödinger equation (NLS) on the torus. Precisely, we prove the super-exponential long …

Exponential stability estimate for the derivative nonlinear Schrödinger equation

H Cong, L Mi, X Wu, Q Zhang - Nonlinearity, 2022 - iopscience.iop.org
Exponential stability estimate for the derivative nonlinear Schrödinger equation Page 1
Nonlinearity PAPER Exponential stability estimate for the derivative nonlinear Schrödinger …

Time quasi-periodic traveling gravity water waves in infinite depth

R Feola, F Giuliani - arXiv preprint arXiv:2011.12794, 2020 - arxiv.org
We present the recent result [8] concerning the existence of quasi-periodic in time traveling
waves for the 2d pure gravity water waves system in infinite depth. We provide the first …