scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
30 Dec 2019
TL;DR: In this paper, the quintic B-spline differential quadrature method (QBDQM) has been used to obtain the numerical approximation of the combined Korteweg-de Vries and modified KORTeweg de Vries equation (combined KdV-mKdV), and the efficiency and effectiveness of the proposed method has been tested by computing the maximum error norm and discrete root mean square error.
Abstract: In this paper, quintic B-spline differential quadrature method (QBDQM) has been used to obtain the numerical approximation of the combined Korteweg-de Vries and modified Korteweg-de Vries equation (combined KdV-mKdV). The efficiency and effectiveness of the proposed method has been tested by computing the maximum error norm L_\infinity and discrete root mean square error L_2 . The newly found numerical approximations have been compared to available numerical approximations and this comparison has shown that the proposed method is an efficient one for solving

5 citations

Journal ArticleDOI
TL;DR: In this article , an approximate solution to the damped quintic-cubic nonlinear Duffing-Mathieu equation via a modified homotopy perturbation method (HPM) is presented.
Abstract: Abstract This paper is devoted to obtain an approximate solution to the damped quintic–cubic nonlinear Duffing–Mathieu equation via a modified homotopy perturbation method (HPM). The modification under consideration deals with the improvement of the HPM with the exponential decay parameter. This scheme allows us to get a solution to the damped nonlinear Duffing–Mathieu equation, which the classical HPM failed to obtain. It is found that the solutions and the characteristic curves are affected by the presence of the damping force. The frequency-amplitude characteristics of a symbiotic solution are confirmed as well as the stability condition is carried out in the (non)-resonance cases. All the calculations are done via Mathematica. The comparison between both of the numerical and analytical solutions showed a very good agreement. Illustrated graphs are plotted for a superior realization of periodic motions in the Duffing–Mathieu oscillator. Nonlinear behaviors of each oscillation motion have been characterized through frequency curves.

5 citations

Journal ArticleDOI
TL;DR: In this article , diverse forms of lump: lump one stripe, lump two stripe, generalized breathers, Akhmediev breather, multiwave, M-shaped rational and rogue wave solutions for the complex cubic quintic Ginzburg Landau (CQGL) equation with intrapulse Raman scattering (IRS) via appropriate transformations approach.
Abstract: This manuscript consist of diverse forms of lump: lump one stripe, lump two stripe, generalized breathers, Akhmediev breather, multiwave, M-shaped rational and rogue wave solutions for the complex cubic quintic Ginzburg Landau (CQGL) equation with intrapulse Raman scattering (IRS) via appropriate transformations approach. Furthermore, it includes homoclinic, Ma and Kuznetsov-Ma breather and their relating rogue waves and some interactional solutions, including an interactional approach with the help of the double exponential function. We have elaborated the kink cross-rational (KCR) solutions and periodic cross-rational (KCR) solutions with their graphical slots. We have also constituted some of our solutions in distinct dimensions by means of 3D and contours profiles to anticipate the wave propagation. Parameter domains are delineated in which these exact localized soliton solutions exit in the proposed model.

5 citations

Journal ArticleDOI
TL;DR: In this paper , the optical solitons for the Kundu-Eckhaus (KE) equation with quintic nonlinearity and Raman effect were studied, and the improved modified extended tanh-function method was applied to obtain many soliton solutions.
Abstract: Our paper studies the optical solitons for the Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying the improved modified extended tanh-function method, many soliton solutions can be obtained such as bright soliton solutions, dark soliton solutions, and the singular soliton solution. In addition, we can obtain various types of solutions, namely, singular periodic solutions, exponential solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some selected solutions are illustrated graphically to show the physical nature and the characteristics of the obtained solutions.

5 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation and can be represented in an infinity of ways, all interconnected by certain nonlinear transformations.
Abstract: This paper shows that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transformations are generic and valid for arbitrary dynamics governed by algebraic equations of motion.

5 citations


Network Information
Related Topics (5)
Differential equation
88K papers, 2M citations
88% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
87% related
Boundary value problem
145.3K papers, 2.7M citations
86% related
Partial differential equation
70.8K papers, 1.6M citations
85% related
Bounded function
77.2K papers, 1.3M citations
85% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202397
2022254
2021109
2020104
201993
201893