Titlebook: Recent Developments in Integrable Systems and Related Topics of Mathematical Physics; Kezenoi-Am, Russia, Victor M. Buchstaber,Sotiris Kon

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,Movable Poles of Painlevé I Transcendents and Singularities of Monodromy Data Manifolds,to the singular submanifold. Such solutions coincide with the class of “truncated” solutions (intégrales tronquée) by classification of P. Boutroux. We derive further classification based on decomposition of singularities of monodromy data manifold.

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Numerical Instability of the Akhmediev Breather and a Finite-Gap Model of It,ves in weakly nonlinear media, considered the main physical mechanism for the appearance of rogue (anomalous) waves (RWs) in Nature. In this paper we study the numerical instabilities of the Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting o

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,Movable Poles of Painlevé I Transcendents and Singularities of Monodromy Data Manifolds,nd between singularities of two-dimensional monodromy data manifold and analytic properties of solutions parametrized by this manifold. It is proved that solutions of Painlevé ?I equation have no poles at infinity at a given critical sector of the complex plane iff the related monodromy data belong

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