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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 quintic B-spline collocation scheme is implemented to find numerical solution of the Kuramoto-Sivashinsky equation, and the accuracy of the proposed method is demonstrated by four test problems.
81 citations
TL;DR: A new means to differentiate among the solutions, namely, the winding number of the closed loop formed by a union of the hodographs of the PH quintic and of the unique “ordinary” cubic interpolant is introduced.
80 citations
TL;DR: In this article, the properties of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrodinger equation (ICQNLSE) with an external potential are studied.
Abstract: Properties of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schr\"odinger equation (ICQNLSE) with an external potential are studied. When it is associated with the homogeneous CQNLSE, a general condition exists linking the external potential and inhomogeneous cubic and quintic (ICQ) nonlinearities. Besides for the nonpresence of an external potential, two classes of Jacobian elliptic periodic potentials are discussed in detail, and the corresponding ICQ nonlinearities are found to be either periodic or localized. Exact analytical soliton solutions in these cases are presented, such as the bright, dark, kink, and periodic solitons, etc. An appealing aspect is that the ICQNLSE can support bound states with any number of solitons when the ICQ nonlinearities are localized and an external potential is either applied or not.
80 citations
TL;DR: In this paper, a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced, which is valid for all fraction values α ⩾ 1, the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time.
80 citations
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TL;DR: In this article, the zeta-functions for a one parameter family of quintic three-folds defined over finite fields and for their mirror manifolds were studied and their structure was analyzed.
Abstract: We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to `see' these curves in the geometry of the quintic. Having these zeta-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the zeta-functions is suggested by an application of the Weil conjectures to Calabi-Yau threefolds: the zeta-functions are rational functions and the degrees of the numerators and denominators are exchanged between the zeta-functions for the manifold and its mirror. It is clear nevertheless that the zeta-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a `quantum modification' of the zeta-function that restores the symmetry between the Kahler and complex structure parameters. We note that the zeta-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion.
79 citations