6533b870fe1ef96bd12cfcd0
RESEARCH PRODUCT
On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
Tamara GravaChristian KleinBoris Dubrovinsubject
Painleve equationsApplied Mathematics010102 general mathematicsGeneral EngineeringGradient catastrophe01 natural sciencesUniversality (dynamical systems)Method of undetermined coefficientsNonlinear Schrodinger equation; Gradient catastrophe; Painleve equationssymbols.namesakeModeling and SimulationModelling and Simulation0103 physical sciencessymbolsInitial value problem0101 mathematics010306 general physicsNonlinear Schrodinger equationNonlinear Schrödinger equationSettore MAT/07 - Fisica MatematicaEngineering(all)MathematicsMathematical physicsdescription
We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schrodinger equation \(i\epsilon \varPsi _{t}+\frac{\epsilon^{2}}{2}\varPsi _{xx}+|\varPsi |^{2}\varPsi =0\) , e ≪1, with analytic initial data of the form \(\varPsi (x,0;\epsilon)=A(x)e^{\frac{i}{\epsilon}S(x)}\) is approximately described by a particular solution to the Painleve-I equation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-06-05 |