𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New singular solutions of the nonlinear Schrödinger equation

✍ Scribed by Gadi Fibich; Nir Gavish; Xiao-Ping Wang

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
1004 KB
Volume
211
Category
Article
ISSN
0167-2789

No coin nor oath required. For personal study only.

✦ Synopsis

We present numerical simulations of a new type of singular solutions of the critical nonlinear Schrödinger equation (NLS), that collapse with a quasi self-similar ring profile at a square root blowup rate. We find and analyze the equation of the ring profile. We observe that the self-similar ring profile is an attractor for a large class of radially-symmetric initial conditions, but is unstable under symmetry-breaking perturbations. The equation for the ring profile admits also multi-ring solutions that give rise to collapsing self-similar multi-ring solutions, but these solutions are unstable even in the radially-symmetric case, and eventually collapse with a single ring profile. Collapsing ring solutions are also observed in the supercritical NLS.

📜 SIMILAR VOLUMES

Singularity analysis and explicit soluti
Singularity analysis and explicit solutions of a new coupled nonlinear Schrödinger type equation
✍ Xuelin Yong; Jianwei Gao; Zhiyong Zhang 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 279 KB

The Painlevé test is performed for a new coupled nonlinear Schrödinger type equation. It is shown that this equation passes the integrability test and is P-integrable. By means of the truncated singular expansions, we construct some novel explicit solutions from the trivial zero solution. Furthermor