Non-generic blow-up solutions for the critical focusing NLS in 1-D

Krieger, Joachim, and Schlag, Wilhelm. "Non-generic blow-up solutions for the critical focusing NLS in 1-D." Journal of the European Mathematical Society 011.1 (2009): 1-125. <http://eudml.org/doc/277450>.

@article{Krieger2009,
abstract = {We consider the $L^2$-critical focusing non-linear Schrödinger equation in $1+1$-d. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow-up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a codimension one stable blow-up manifold in the measurable category.},
author = {Krieger, Joachim, Schlag, Wilhelm},
journal = {Journal of the European Mathematical Society},
keywords = {nonlinear Schrödinger equations; $L^2$-critical NLS; pseudo-conformal blow-up; nonlinear Schrödinger equation; collapse; conformal invariance; symplectic structure; root space},
language = {eng},
number = {1},
pages = {1-125},
publisher = {European Mathematical Society Publishing House},
title = {Non-generic blow-up solutions for the critical focusing NLS in 1-D},
url = {http://eudml.org/doc/277450},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Krieger, Joachim
AU - Schlag, Wilhelm
TI - Non-generic blow-up solutions for the critical focusing NLS in 1-D
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 1
SP - 1
EP - 125
AB - We consider the $L^2$-critical focusing non-linear Schrödinger equation in $1+1$-d. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow-up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a codimension one stable blow-up manifold in the measurable category.
LA - eng
KW - nonlinear Schrödinger equations; $L^2$-critical NLS; pseudo-conformal blow-up; nonlinear Schrödinger equation; collapse; conformal invariance; symplectic structure; root space
UR - http://eudml.org/doc/277450
ER -