Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.

Explicit lifts of quintic Jacobi sums and period polynomials for Fq

Abstract: In this paper, we construct explicit lifts of quintic Jacobi sums for finite fields via integer solutions of Dickson's system Namely we give a procedure to compute quintic Jacobi sums for extended field FP s+t by using quintic Jacobi sums for F Ps and for F pt . We also have the multiplication formula from F ps to F p ns as a special case. By the quintuplication formula, we obtain the explicit factorization of the quintic period polynomials for finite fields.

Computing contours by successive solution of quintic polynomial equations

Abstract: By a method known from fimte-element theory, bivariate qumtic interpolation polynomials can be determined over triangles (18-degree-of-freedom element with value, slope, and curvature parameters in the nodes). The connections to neighboring polynomials are continuous and smooth. A new method is discussed for computing contour hnes directly from the polynomial coefficients found for each triangle by solving a nonlinear equation for every point of a line. The lines are computed triangle by triangle so that in principal true parallel operation on all triangles is possible. The method is superior in methodical and operational aspects over the traditional way where values are computed over a rectangular grid prior to contour plotting.

A quintic polynomial differential system with eleven limit cycles at the infinity

Abstract: In this article, a recursion formula for computing the singular point quantities of the infinity in a class of quintic polynomial systems is given. The first eleven singular point quantities are computed with the computer algebra system Mathematica. The conditions for the infinity to be a center are derived as well. Finally, a system that allows the appearance of eleven limit cycles in a small enough neighborhood of the infinity is constructed.

Stability analysis of the soliton solutions for the generalized quintic derivative nonlinear Schrödinger equation

Abstract: The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrodinger (DNLS) equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated.