Quintic function

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

Equivalence among orbital equations of polynomial maps

Abstract: This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transformations are generic, valid for arbitrary dynamics governed by algebraic equations of motion.

A new quintic B-spline approximation for numerical treatment of Boussinesq equation

Abstract: In this work, we have presented a new quintic B-spline approximation technique for numerical solution of Boussinesq equation. Usual finite difference formulation has been applied to discretize the problem in temporal domain, whereas, the typical fifth degree B-spline functions, equipped with a new approximation for fourth order derivative, have been utilized to interpolate the unknown function in spatial direction. The stability and error analysis of the proposed numerical algorithm have been studied rigorously. Two test examples are considered to affirm the performance and accuracy of the new scheme. The computational outcomes are found to be better than the existing numerical techniques on the topic.

Une quintique numérique réelle dont le premier nombre de Betti est maximal

Abstract: For a real numerical quintic surface X, the first Betti number b1(ℝX) of the real point set ℝX is bounded by 47. We show the existence of a real numerical quintic surface X such that b1(ℝX)=47. We also construct a real numerical quintic surface whose real point set has 23 connected components.

Complex plane representations and stationary states in cubic and quintic resonant systems

Abstract: Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have constructed a large class of such resonant systems (with specific representatives related to the physics of Bose-Einstein condensates and Anti-de Sitter spacetime) that admit special analytic solutions and an extra conserved quantity. Here, we develop and explore a complex plane representation for these systems modelled on the related cubic Szego and LLL equations. To demonstrate the power of this representation, we use it to give simple closed form expressions for families of stationary states bifurcating from all individual modes. The conservation laws, the complex plane representation and the stationary states admit furthermore a natural generalization from cubic to quintic nonlinearity. We demonstrate how two concrete quintic PDEs of mathematical physics fit into this framework, and thus directly benefit from the analytic structures we present: the quintic nonlinear Schroedinger equation in a one-dimensional harmonic trap, studied in relation to Bose-Einstein condensates, and the quintic conformally invariant wave equation on a two-sphere, which is of interest for AdS/CFT-correspondence.