Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors obtained the most general one-dimensional classical systems with a third and a fourth order ladder operator satisfying polynomial Heisenberg algebras, written in terms of the solutions of quartic and quintic equations.
Abstract: We recall results concerning one-dimensional classical and quantum systems with ladder operators. We obtain the most general one-dimensional classical systems respectively with a third and a fourth order ladder operators satisfying polynomial Heisenberg algebras. These systems are written in terms of the solutions of quartic and quintic equations. We use these results to present two new families of superintegrable systems and examples of trajectories that are deformed Lissajous's figures.
24 citations
TL;DR: In this article, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubic-quintic Duffing oscillator.
Abstract: In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubic-quintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability.
24 citations
TL;DR: In this paper, the authors consider the defocusing quintic nonlinear Schrodinger equation in four space dimensions and prove that any solution that remains bounded in the critical Sobolev space must be global and scatter.
23 citations
TL;DR: A branch-blending strategy is applied to model the bifurcation such that the coherence among the individual branching segments is characterized and the conditions for the twist-compatibility from the requirements of cross-boundary tangential continuity are derived.
23 citations
TL;DR: From the classical Voronoi algorithm, an algorithm to classify quadratic positive definite forms by their minimal vectors is derived; some new invariants for a class are defined, for which several conjectures are proposed.
Abstract: From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.
23 citations