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 paper, the authors discuss local Hermite interpolation by C^2 quintic Powell-Sabin splines represented in a normalized B-spline basis and derive explicit formulae for the spline coefficients to interpolate given Hermite data.
14 citations
14 citations
TL;DR: In this article, the dromion-like excitations corresponding to intramolecular chain-like proteins are described by using cubic-quintic nonlinear Schrodinger equation (CQNSE) governing the dynamics of proteins.
Abstract: We investigate the dromion-like excitations corresponding to intramolecular chain-like proteins. In the present work, the dromion-like excitations are described by using cubic-quintic nonlinear Schrodinger equation (CQNSE) governing the dynamics of proteins and we analytically analyze the velocity (v) of dromion-like structure compared with velocity (
$$v_a$$
) of acoustical sound waves corresponding to the longitudinal vibrations of protein molecules. Our work is motivated by the effectiveness and powerful mathematical techniques such as modified extended tanh function method and sine–cosine function method for solving CQNSE to obtain dromion-like structures.
14 citations
TL;DR: In this article , the Hirota bilinear method was used to study soliton interactions of quasi-1D Bose-Einstein Condensate system (BECs) with dipole-dipole attraction and repulsion.
Abstract: With the help of the Hirota bilinear method (HBM), we study soliton interactions of quasi-1D Bose-Einstein Condensate system (BECs) with dipole-dipole attraction and repulsion. BEC is an extended form of nonlinear Schrödinger equation (NLSE) and it consists of quadratic-cubic nonlinearities, linear gain or loss and time modulated dispersion. Due to its spatially varying coefficients property it has significance in the field of fluid dynamics, classical and quantum field theories, nonlinear optics and physics etc. We will also discuss soliton interactions with graphically descriptions for QDNLSE. We obtain some parabolic, anti parabolic, M-shaped, W-shaped, butterflies, bright, anti dark, V-shaped, S-shaped and other solitons for our governing models.
14 citations
TL;DR: In this article, the problem of finding closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations is addressed. But the problem is not solved by the truncation method, since no solution can be missed, and the involved work requires computer algebra.
Abstract: Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations The suitable methods, which can only be nonperturbative, are classified in two classes
In the first class, which includes the well known so-called truncation methods, one \textit{a priori} assumes a given class of expressions (polynomials, etc) for the unknown solution; the involved work can easily be done by hand but all solutions outside the given class are surely missed
In the second class, instead of searching an expression for the solution, one builds an intermediate, equivalent information, namely the \textit{first order} autonomous ODE satisfied by the solitary wave; in principle, no solution can be missed, but the involved work requires computer algebra
We present the application to the cubic and quintic complex one-dimensional Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation
14 citations