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: In this article, the authors presented explicit exact solutions of the high-order nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses.
Abstract: By using the extended hyperbolic auxiliary equation method, we present explicit exact solutions of the high-order nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. These solutions include trigonometric function type and exact solitary wave solutions of hyperbolic function type. Among these solutions, some are found for the first time.
43 citations
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TL;DR: An accurate closed-form solution for the quintic Duffing equation is obtained using a cubication method and excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed.
42 citations
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TL;DR: In this paper, the Korteweg-de Vries-Burgers (KdVB) equation is solved numerically by anew differential quadrature method based on quintic B-spline functions.
Abstract: In this paper, the Korteweg-de Vries-Burgers’ (KdVB) equation is solved numerically by anew differential quadrature method based on quintic B-spline functions. The weightingcoefficients are obtained by semi-explicit algorithm including an algebraic system with fivebandcoefficient matrix. The L2 and L∞ error norms and lowest three invariants 1 2 I , I and3 I have computed to compare with some earlier studies. Stability analysis of the method isalso given. The obtained numerical results show that the present method performs better thanthe most of the methods available in the literature.
42 citations
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TL;DR: The problem of constructing a plane polynomial curve with given end points and end tangents, and a specified arc length, and an algorithm to construct interpolants to planar G1 Hermite data, with exact prescribed arc lengths is presented.
42 citations
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TL;DR: In this article, the authors construct families of fundamental, dipole, and tripole solitons in the fractional Schrodinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos 2 x and sin 2 x, respectively.
Abstract: We construct families of fundamental, dipole, and tripole solitons in the fractional Schrodinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos 2 x and sin 2 x , respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the Levy index (LI) that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.
42 citations