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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: In this paper, the supratransmission phenomenon in the discrete nonlinear Schrodinger equation with the cubic-quintic nonlinearity was numerically analyzed, and it was shown that the lattice induces the generation of the train of dark solitons carried by a traveling kink and the traveling Kink for chosen driving amplitude.
Abstract: We numerically analyzed the supratransmission phenomenon in the discrete nonlinear Schrodinger equation with the cubic–quintic nonlinearity. It has been reported that the homoclinic nonlinear band-gap threshold matches very well with the model. In the case of the cooperation between the nonlinearities (self-focusing cubic and quintic terms), the train of discrete band-gap waves overcomes the potential barrier of the first sites before merging or rebounding. In the case of competing self-focusing cubic and defocusing quintic nonlinearities, it is found that the lattice induces the generation of the train of dark solitons carried by a traveling kink and the traveling kink for chosen driving amplitude.
20 citations
TL;DR: The solution of the nonlinear differential equation Y(x, Y, Y) with two-point boundary conditions is approximated by a quintic or cubic spline function y(x), which is well suited to nonuniform mesh size and dynamic mesh size allocation.
Abstract: The solution of the nonlinear differential equation Y″ = F(x, Y, Y′) with two-point boundary conditions is approximated by a quintic or cubic spline function y(x). The method is well suited to nonuniform mesh size and dynamic mesh size allocation. For uniform mesh size h, the error in the quintic spline y(x) is O(h4), with typical error one-third that from Numerov's method. Requiring the differential equation to be satisfied at the mesh points results in a set of difference equations, which are block tridiagonal and so are easily solved by relaxation or other standard methods.
20 citations
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TL;DR: In this paper, the fundamental relationship between stable quotient invariants and the B-model for local CP2 in all genera was studied and a direct geometric proof of the holomorphic anomaly equation was given.
Abstract: We study the fundamental relationship between stable quotient invariants and the B-model for local CP2 in all genera. Our main result is a direct geometric proof of the holomorphic anomaly equation in the precise form predicted by B-model physics. The method yields new holomorphic anomaly equations for an infinite class of twisted theories on projective spaces. An example of such a twisted theory is the formal quintic defined by a hyperplane section of CP4 in all genera via the Euler class of a complex. The formal quintic theory is found to satisfy the holomorphic anomaly equations conjectured for the true quintic theory. Therefore, the formal quintic theory and the true quintic theory should be related by transformations which respect the holomorphic anomaly equations.
20 citations
TL;DR: An analytical solution of the damped cubic-quintic Duffing oscillator is derived which is based on a rational elliptic form used to obtain exact and approximate solutions of undamped oscillators and it is shown that theoretical predictions compares well with the numerical integration solutions obtained by a fourth order Runge-Kutta method.
19 citations
TL;DR: The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation as discussed by the authors , and two simplified formulations are suggested.
Abstract: The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory.
19 citations