[CITATION][C] Semilinear Schrodinger equations

T Cazenave - New York University, Courant Institute of …, 2003 - books.google.com
The nonlinear Schrodinger equation has received a great deal of attention from
mathematicians, particularly because of its applications to nonlinear optics. It is also a good …

[BOOK][B] Nonlinear dispersive equations: local and global analysis

T Tao - 2006 - books.google.com
Among nonlinear PDEs, dispersive and wave equations form an important class of
equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation …

Is Physics Informed Loss Always Suitable for Training Physics Informed Neural Network?

C Wang, S Li, D He, L Wang - Advances in Neural …, 2022 - proceedings.neurips.cc
Abstract The Physics-Informed Neural Network (PINN) approach is a new and promising
way to solve partial differential equations using deep learning. The $ L^ 2$ Physics-Informed …

KdV is well-posed in

R Killip, M Vişan - Annals of Mathematics, 2019 - projecteuclid.org
We prove global well-posedness of the Korteweg--de Vries equation for initial data in the
space H^-1(R). This is sharp in the class of H^s(R) spaces. Even local well-posedness was …

The Cauchy problem for the Novikov equation

AA Himonas, C Holliman - Nonlinearity, 2012 - iopscience.iop.org
This work studies the initial value problem for a Camassa–Holm type equation with cubic
nonlinearities that has been recently discovered by Vladimir Novikov to be integrable. For s> …

Well-posedness and scattering for the KP-II equation in a critical space

M Hadac, S Herr, H Koch - Annales de l'Institut Henri Poincaré C, Analyse …, 2009 - Elsevier
The Cauchy problem for the Kadomtsev–Petviashvili-II equation [Formula: see text] is
considered. A small data global well-posedness and scattering result in the scale invariant …

Global wellposedness of KdV in

T Kappeler, P Topalov - 2006 - projecteuclid.org
GLOBAL WELLPOSEDNESS OF KdV IN H (T,R) Page 1 GLOBAL WELLPOSEDNESS OF
KdV IN H −1 (T,R) T. KAPPELER and P. TOPALOV Abstract By the inverse method we show …

Ill-posedness for nonlinear Schrodinger and wave equations

M Christ, J Colliander, T Tao - arxiv preprint math/0311048, 2003 - arxiv.org
The nonlinear wave and Schrodinger equations on Euclidean space of any dimension, with
general power nonlinearity and with both the focusing and defocusing signs, are proved to …

[BOOK][B] Modulation spaces

Á Bényi, KA Okoudjou, Á Bényi, KA Okoudjou - 2020 - Springer
Modulation Spaces | SpringerLink Skip to main content Advertisement SpringerLink
Account Menu Find a journal Publish with us Track your research Search Cart Book cover …

On the local well-posedness of the Benjamin-Ono equation in Hs(ℝ)

H Koch, N Tzvetkov - International Mathematics Research …, 2003 - academic.oup.com
On the local well-posedness of the Benjamin-Ono equation in Hs(R) Page 1 IMRN
International Mathematics Research Notices 2003, No. 26 On the Local Well-Posedness of …