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On critical behaviour in systems of Hamiltonian partial differential equations

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dc.contributor.author Dubrovin, Boris
dc.contributor.author Grava, Tamara
dc.contributor.author Klein, Christian
dc.contributor.author Moro, Antonio
dc.date.accessioned 2014-01-15T07:53:33Z
dc.date.available 2014-01-15T07:53:33Z
dc.date.issued 2014-01-15
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/7243
dc.description.abstract We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.title On critical behaviour in systems of Hamiltonian partial differential equations en_US
dc.type Preprint en_US
dc.subject.miur MAT/07 FISICA MATEMATICA
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US


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