Topic
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: Methods for approximating circular arcs using quintic polynomial curves with G2, G3, or G4 continuities at the circular arc's ends are presented.
49 citations
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TL;DR: In this paper, the authors considered the problem of large data scattering for the quintic nonlinear Schrodinger equation on R \times \T^2 and proposed a large scale profile that controls the asymptotic behavior of the solutions.
Abstract: We consider the problem of large data scattering for the quintic nonlinear Schrodinger equation on $\R \times \T^2$. This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a "large scale profile") that controls the asymptotic behavior of the solutions.
49 citations
TL;DR: Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%.
Abstract: In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtained using the Homotopy Analysis Method (HAM) and Homotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%.
48 citations
TL;DR: In this article, the quintic non-linear Schrodinger equation on a two-dimensional torus is studied and a sufficiently simple toy model is proposed for the case of cubic NLS.
Abstract: We study the quintic Non Linear Schrodinger equation on a two dimensional torus and exhibit orbits whose Sobolev norms grow with time. The main point is to reduce to a sufficiently simple toy model, similar in many ways to the one discussed in [15] for the case of the cubic NLS. This requires an accurate combinatorial analysis.
48 citations
TL;DR: In this paper, the fundamental solitary wave in a cubic-quintic nonlinear medium is investigated both numerically and variationally, and an equivalent particle model is used to understand the behaviour of the numerical solutions, and while a super-Gaussian trial function has only a limited range of applicability in the variational analysis, a supersech trial function is found to match the numerical solution well for all input powers.
Abstract: Fundamental solitary waves in a cubic-quintic nonlinear medium are investigated both numerically and variationally. An equivalent particle model is used to understand the behaviour of the numerical solutions, and while a super-Gaussian trial function is found to have only a limited range of applicability in the variational analysis, a super-sech trial function is found to match the numerical solutions well for all input powers. Various limits are also investigated.
48 citations