Topic
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: In this paper, the Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic three-folds were studied.
Abstract: We study the Clifford type inequality for a particular type of curves $$C_{2,2,5}$$
, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov–Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macri, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in $$\mathbf {P}^4_{\mathbb {C}}$$
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65 citations
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TL;DR: In this paper, three-dimensional analytical optical soliton solutions are found based on some high-order nonlinear Schrodinger equations, and the stability of solitons in the cubic-quintic nonlinear case is better than that in cubic nonlinear cases, but worse than the cubic quintic-septimal case.
Abstract: Under parity-time symmetric potentials, different-order nonlinearities such as cubic, quintic and septimal nonlinearities, altogether with their combinations and second-order and fourth-order dispersions/diffractions are simultaneously considered to form three-dimensional optical solitons. Based on some high-order nonlinear Schrodinger equations, three-dimensional analytical optical soliton solutions are found. In the defocusing cubic nonlinear case, three-dimensional optical soliton without fourth-order diffraction/dispersion is stable than that with fourth-order diffraction/dispersion. However, in the defocusing cubic and focusing quintic nonlinear case, the stability situation of soliton is just on the contrary. Among all combinations of nonlinearity, the stability of three-dimensional optical soliton in the cubic-quintic nonlinear case is better than that in the cubic nonlinear case, but worse than that in the cubic-quintic-septimal nonlinear case. In the quintic-septimal nonlinear case, three-dimensional optical soliton is unstable and will collapse ultimately.
64 citations
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TL;DR: In this article, the authors present an algorithm able to provide in closed form all those travelling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational.
Abstract: In order to flnd analytically the travelling waves of partially integrable au- tonomous nonlinear partial difierential equations, many methods have been pro- posed over the ages: \projective Riccati method", \tanh-method", \exponential method", \Jacobi expansion method",
ew ...", etc. The common default to all these \truncation methods" is to only provide some solutions, not all of them. By implementing three classical results of Briot, Bouquet and Poincare, we present an algorithm able to provide in closed form all those travelling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational. Our examples here include the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.
64 citations
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TL;DR: In this paper, the existence, stability, and mobility of fundamental discrete solitons in two-and three-dimensional nonlinear Schrodinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities were investigated.
63 citations
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TL;DR: In this article, a large set of exact analytic traveling-wavesolutions for the equation iut + uxx = a1u|u|2 + a2u| u|4 that can be of interest in higher-order nonlinear-optical media is presented.
Abstract: We present a large set of exact analytic traveling-wavesolutions for the equation iut + uxx = a1u|u|2 + a2u|u|4 that can be of interest in higher-order nonlinear-optical media. This set includes all bright and dark solitary waves as well as periodic ones. Our procedure consists of direct integration; it is then purely algebraic and simple. Solutions are given in simple forms and tabulated.
62 citations