On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\it tritronquée} solution to the Painlevé-I equation

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dc.creatorDubrovin, B.
dc.creatorGrava, T.
dc.creatorKlein, C.
dc.date2007-04-04
dc.date2007-05-15
dc.date.accessioned2026-07-07T08:01:16Z
dc.date.available2026-07-07T08:01:16Z
dc.descriptionWe argue that the critical behaviour near the point of ``gradient catastrophe" of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation $ iεψ_t +\frac{ε^2}2ψ_{xx}+ |ψ|^2 ψ=0$ with analytic initial data of the form $ψ(x,0;ε) =A(x) e^{\frac{i}ε S(x)}$ is approximately described by a particular solution to the Painlevé-I equation.
dc.description32 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/0704.0501
dc.identifierhttp://arxiv.org/abs/0704.0501
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128860
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleOn universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\it tritronquée} solution to the Painlevé-I equation
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