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)
SN - 0938-8974
VL - 19
SP - 57
EP - 94
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
IS - 1
ER -