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Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms in this article, where a careful discussion of the underlying virtual intersection theory is included.
Abstract: Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Vafa multiple cover formula is used to define virtually enumerative disk invariants. The results may also be viewed as providing a virtual enumeration of real rational curves on the quintic.
15 citations
TL;DR: In this article, it was shown that any meromorphic solution of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation is necessarily elliptic or degenerate elliptic.
Abstract: We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie’s lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.
15 citations
TL;DR: In this article, the authors constructed two small resolutions of singularities of the Coble fourfold (the double cover of the four-dimensional projective space branched over the Igusa quartic) and used them to show that all $S_6$-invariant three-dimensional quartics are birational to conic bundles over the quintic del Pezzo surface with the discriminant curves from the Wiman-Edge pencil.
Abstract: We construct two small resolutions of singularities of the Coble fourfold (the double cover of the four-dimensional projective space branched over the Igusa quartic). We use them to show that all $S_6$-invariant three-dimensional quartics are birational to conic bundles over the quintic del Pezzo surface with the discriminant curves from the Wiman-Edge pencil. As an application, we check that $S_6$-invariant three-dimensional quartics are unirational, obtain new proofs of rationality of four special quartics among them and irrationality of the others, and describe their Weil divisor class groups as $S_6$-representations.
15 citations
TL;DR: In this article, stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign is explored.
Abstract: We explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign This setting can be implemented in optical waveguides based on colloids of nanoparticles The solitons stability is identified by solving linearized equations for small perturbations, and is found to fully comply with the Vakhitov-Kolokolov criterion In the limit case of tight confinement of the nonlinearity, results are obtained in an analytical form, approximating the confinement profile by a delta-function It is found that the confinement greatly increases the largest total power of stable solitons, in the case when the quintic term is defocusing, which suggests a possibility to create tightly confined high-power light beams guided by the spatial modulation of the local nonlinearity strength
15 citations
TL;DR: An algorithm which determines a bivariate smooth piecewise polynomial interpolant to function values given at points scattered in R 2fs so that the degree of the polynomials will be as small as possible for arbitrary triangulations and a high degree ofPolynomial precision is achieved.
15 citations