TY - JOUR

T1 - On Universality of Critical Behavior in the Focusing Nonlinear Schrödinger Equation, Elliptic Umbilic Catastrophe and the Tritronquée Solution to the Painlevé-I Equation

AU - Dubrovin, B.

AU - Grava, Tamara

AU - Klein, C

PY - 2009/2

Y1 - 2009/2

N2 - 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.

AB - 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.

U2 - 10.1007/s00332-008-9025-y

DO - 10.1007/s00332-008-9025-y

M3 - Article (Academic Journal)

VL - 19

SP - 57

EP - 94

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 1

ER -