Near soliton dynamics and singularity formation for $ L^2$ critical problems

DOI10.1070/RM2014V069N02ABEH004888zbMath1304.35650arXiv1412.2375OpenAlexW3098599510MaRDI QIDQ2875027

Jérémie Szeftel, Pierre Raphaël, Frank Merle, Yvan Martel

Publication date: 13 August 2014

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.2375

zbMATH Keywords

blowupsolitongeneralized Korteweg-de Vries equationnon-linear Schrödinger equationblowup profilequalitative behaviour of solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Traveling wave solutions (35C07) Soliton solutions (35C08)

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Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5 ⋮ Stable shock formation for nearly simple outgoing plane symmetric waves ⋮ Formation of singularities in nonlinear dispersive PDEs ⋮ Threshold for blowup and stability for nonlinear Schrödinger equation with rotation ⋮ Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation ⋮ Instability of ground states for the NLS equation with potential on the star graph

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