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Regular version of the site
Of all publications in the section: 24
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Article
Smirnov A., Matveenko S., Semenova E. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2015. Vol. 11.

In the article, we describe three-phase finite-gap solutions of the focusing nonlinear Schrödinger equation and Kadomtsev-Petviashvili and Hirota equations that exhibit the behavior of almost-periodic ''freak waves''. We also study the dependency of the solution parameters on the spectral curves.

Added: Oct 15, 2015
Article
Cruz Morales J. A., Galkin S. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2013. Vol. 9. No. 005. P. 1-13.

In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper bounds from [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1–52].

Added: May 27, 2013
Article
Nirov K. S., Razumov A. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2019. Vol. 15. No. 68. P. 1-67.

Hurwitz spaces are spaces of meromorphic functions with prescribed orders of poles on curves of a given genus. In this article, we derive new formulas for the degrees of the strata of Hurwitz spaces of genus 0 corresponding to functions that have two degenerate critical values with prescribed partitions of multiplicities of the preimages. More precisely, one of the critical values has an arbitrary multiplicity of the preimages, while the other is the simplest degenerate critical value.

Added: Nov 26, 2019
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