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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 authors provided explicit error estimates between a given function x ∈ PC ( n ) [a, b ], 2 ≤ n ≤ 6 and its quintic spline interpolate S Δ x ( t ).
Abstract: The purpose of this paper is to provide explicit error estimates between a given function x ( t ∈ PC ( n ) [ a, b ], 2 ≤ n ≤ 6 and its quintic spline interpolate S Δ x ( t ). The results obtained are sharp and improve on, or supplement, those established by Hall [1] and Schultz [2]. These results are then used to acquire precise error bounds for the approximated and biquintic spline interpolates. Sufficient numerical illustration which dwells upon the importance of the obtained results is also included.
28 citations
TL;DR: A family of Class II RRMF quintics is thereby newly identified, that correspond to the case where a(t),b(t) are linear, and have five degrees of freedom, as with the Class I curves.
28 citations
TL;DR: In this paper, the Kudryashov method and generalized tanh method (GTM) are employed to retrieve the new distinct optical solitons for highly dispersive NLSE.
Abstract: In this paper, the Kudryashov’s method and generalized tanh method (GTM) are employed to retrieve the new distinct optical solitons for highly dispersive NLSE. These two schemes effectively acquire the exact solution of the model in the form of dark, singular, singular periodic and bright-singular combo optical solitons. These solutions assist the mathematicians and physicians to realize the physical phenomena of present model. The solutions in presents work indicate that these schemes offer us an influential mathematical tools for solving NLSEs in various areas of applied sciences. In addition, the graphical illustrations of some solutions are also illustrated.
28 citations
TL;DR: In this paper, the cubic-quintic nonlinear Schrodinger equation of up to three dimensions is considered and the cubic nonlinearity is thereby focusing while the quintic one is defocusing, ensuring global well-po...
Abstract: We consider the cubic-quintic nonlinear Schrodinger equation of up to three space dimensions. The cubic nonlinearity is thereby focusing while the quintic one is defocusing, ensuring global well-po...
28 citations
TL;DR: In this article, a systematic analysis of self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients is presented.
Abstract: We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.
28 citations