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pro vyhledávání: '"Grinevich, P. G."'
Autor:
Grinevich, P. G., Novikov, R. G.
{We give a short review of old and recent results on scatterers with transmission eigenvalues of infinite multiplicity, including transparent scatterers. Historically, these studies go back to the publications: Regge (Nuovo Cimento 14, 1959), Newton
Externí odkaz:
http://arxiv.org/abs/2407.16451
The integrable focusing Davey-Stewarson (DS) equations, multidimensional generalizations of the focusing cubic nonlinear Schr\"odinger (NLS) equation, provide ideal mathematical models for describing analytically the dynamics of 2+1 dimensional anoma
Externí odkaz:
http://arxiv.org/abs/2308.12422
Autor:
Grinevich, P. G., Santini, P. M.
The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of $1+1$ dimensional quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism
Externí odkaz:
http://arxiv.org/abs/2206.11950
Autor:
Abenda, Simonetta, Grinevich, Petr G.
The standard parametrization of totally non-negative Grassmannians was obtained by A. Postnikov [45] introducing the boundary measurement map in terms of discrete path integration on planar bicolored (plabic) graphs in the disk. An alternative parame
Externí odkaz:
http://arxiv.org/abs/2111.05782
Autor:
Grinevich, P. G., Novikov, R. G.
We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions $d=2$ and $d=3$. We show that for these scatterers: 1) each positive energy $E$ is a transmission eigenvalue (
Externí odkaz:
http://arxiv.org/abs/2108.08361
Autor:
Abenda, Simonetta, Grinevich, Petr G.
Following [42], positroid cells ${\mathcal S}_{\mathcal M}^{\mbox{TNN}}$ in totally non-negative Grassmannians ${Gr^{\mbox{TNN}} (k,n)}$ admit parametrizations by positive weights on planar bicolored directed perfect networks in the disk. An explicit
Externí odkaz:
http://arxiv.org/abs/2108.03229
Autor:
Grinevich, P. G., Santini, P. M.
The Akhmediev breather (AB) and its M-soliton generalization $AB_M$ are exact solutions of the focusing NLS equation periodic in space and exponentially localized in time over the constant unstable background; they describe the appearance of $M$ unst
Externí odkaz:
http://arxiv.org/abs/2011.11402
Autor:
Abenda, Simonetta, Grinevich, Petr G.
In this paper we construct an explicit map from planar bicolored (plabic) trivalent graphs representing a given irreducible positroid cell $S$ in the totally non-negative Grassmannian $Gr^{\mbox{TNN}}(k,n)$ to the spectral data for the relevant class
Externí odkaz:
http://arxiv.org/abs/2002.04865
Autor:
Grinevich, P. G., Novikov, R. G.
We continue to develop the method for creation and annihilation of contour singularities in the $\bar\partial$--spectral data for the two-dimensional Schr\"odinger equation at fixed energy. Our method is based on the Moutard-type transforms for gener
Externí odkaz:
http://arxiv.org/abs/1911.09627
Publikováno v:
Phys. Rev. E 101, 032204 (2020)
The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism for the appearence
Externí odkaz:
http://arxiv.org/abs/1910.13176