On Universality of Critical Behavior in the Focusing Nonlinear Schrödinger Equation, Elliptic Umbilic Catastrophe and the Tritronquée Solution to the Painlevé-I Equation

B. Dubrovin, Tamara Grava, C Klein

Research output: Contribution to journalArticle (Academic Journal)peer-review

69 Citations (Scopus)

Abstract

We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation iϵΨ t +ϵ 2 2 Ψ xx +|Ψ| 2 Ψ=0 , ε≪1, with analytic initial data of the form Ψ(x,0;ϵ)=A(x)e i ϵ S(x) is approximately described by a particular solution to the Painlevé-I equation.
Original languageEnglish
Pages (from-to)57-94
Number of pages38
JournalJournal of Nonlinear Science
Volume19
Issue number1
DOIs
Publication statusPublished - Feb 2009

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