This is a brief introduction to the joint work with Wilhelm Schlag and Joachim Krieger on the global dynamics for nonlinear dispersive equations with unstable ground states. We prove that the center-stable and the center-unstable manifolds of the ground state solitons separate the energy space by the dynamical property into the scattering and the blow-up regions, respectively in positive time and in negative time. The transverse intersection of the two manifolds yields nine sets of global dynamics, which include stable transition from blow-up to scattering and vice versa.
Keywords: nonlinear wave equations, nonlinear Schrödinger equation, nonlinear Klein-Gorond equation, solitons, scattering theory, blow-up, invariant manifolds
@article{JEDP_2012____A8_0, author = {Nakanishi, Kenji}, title = {Global dynamics beyond the ground state energy for nonlinear dispersive equations}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {8}, pages = {1--6}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2012}, doi = {10.5802/jedp.91}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.91/} }
TY - JOUR AU - Nakanishi, Kenji TI - Global dynamics beyond the ground state energy for nonlinear dispersive equations JO - Journées équations aux dérivées partielles PY - 2012 SP - 1 EP - 6 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.91/ DO - 10.5802/jedp.91 LA - en ID - JEDP_2012____A8_0 ER -
%0 Journal Article %A Nakanishi, Kenji %T Global dynamics beyond the ground state energy for nonlinear dispersive equations %J Journées équations aux dérivées partielles %D 2012 %P 1-6 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.91/ %R 10.5802/jedp.91 %G en %F JEDP_2012____A8_0
Nakanishi, Kenji. Global dynamics beyond the ground state energy for nonlinear dispersive equations. Journées équations aux dérivées partielles (2012), article no. 8, 6 p. doi : 10.5802/jedp.91. http://www.numdam.org/articles/10.5802/jedp.91/
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