Quintic function

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

Mapping between generalized nonlinear Schrödinger equations and neutral scalar field theories and new solutions of the cubic-quintic NLS equation

Abstract: We highlight an interesting mapping between the moving breather solutions of the generalized nonlinear Schrodinger (NLS) equations and the static solutions of neutral scalar field theories. Using this connection, we then obtain several new moving breather solutions of the cubic–quintic NLS equation both with and without uniform phase in space. The stability of some stationary solutions is investigated numerically and the results are confirmed via dynamical evolution.

Subcritical Hopf and saddle-node bifurcations in hunting motion caused by cubic and quintic nonlinearities: experimental identification of nonlinearities in a roller rig

Abstract: Railway vehicles suffer from hunting motion, even when traveling below the critical speed obtained by linear analysis, due to the nonlinear characteristics of the wheel system. Nonlinear characteristics in Hopf bifurcations can be characterized as subcritical or supercritical, depending on whether the cubic nonlinearity is softening or hardening, respectively. In a system with softening cubic nonlinearity, third-order nonlinear analysis cannot detect nontrivial stable steady-state oscillations because they are affected by quintic nonlinearity. Therefore, in such a system, it is necessary to apply fifth-order nonlinear analysis to a system model in which quintic nonlinearity is taken into account. In this study, we investigated the cubic and quintic nonlinear phenomena in hunting motion with a roller rig that is widely used for hunting motion research. Previous experimental studies using a roller rig were restricted to the linear stability and the cubic nonlinear stability. We clarified that roller rig experiments can observe the hysteresis phenomenon and the existence of subcritical Hopf and saddle-node bifurcations, indicating that not only the cubic but also the quintic nonlinearity of the wheel system plays an important role. In addition, we obtained the normal form governing the nonlinear dynamics. We developed an experimental identification method to obtain the coefficients of the normal form. The validity of our method was confirmed by comparing the bifurcation diagrams obtained from the experimental time history and the normal form whose coefficients were experimentally identified using the proposed method.

A polynomial Hermite interpolant for C 2 quasi arc-length approximation

Abstract: Transcendental curves, or in general those resulting from offsetting, do not admit an exact rational or polynomial representation and must hence be approximated in order to incorporate them into most commercial CAD systems. We present a simple, yet general geometric tool for polynomial approximation, based on piecewise Hermite interpolation with C 2 quasi arc-length parameterization, a desirable property for robotics or CNC. We take the osculatory Hermite interpolation, prescribing position, tangent direction and curvature at the endpoints, and add quasi arc-length conditions, by imposing unit speed and vanishing tangential acceleration. These new conditions fit naturally into this scheme, yielding a quintic with Bezier points that turn out to display extremely simple geometry. In addition we consider a lower degree alternative to the quintic, namely a cubic B-spline. Finally, we include two examples of applications (the approximations of regular offsets and the clothoid) and compare our results with those from commercial systems or existing methods. Transcendental curves and most offsets do not admit exact NURBS representation.We apply Hermite interpolation to achieve C 2 quasi arc-length approximation.Two alternative tools are considered: piecewise Bezier quintics and cubic B-splines.The quintic displays simple control points, with locally nonparametric arrangement.We approximate offsets and clothoids and compare our results with existing software.

Classifying Brumer's quintic polynomials by weak Mordell-Weil groups

Abstract: We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.