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: A comprehensive analysis of the existence of solutions in the case of spatial PH quintics with end derivatives of equal magnitude is presented, establishing that a two–parameter family of interpolants exists for any prescribed end points, end tangents, and total arc length.
21 citations
TL;DR: In this article, Fisher-Kolmogorov equation is solved numerically by adopting a differential quadrature technique that uses quintic B-spline as the basis functions for space integration.
Abstract: In the present manuscript, Fisher-Kolmogorov equation is solved numerically by adopting a differential quadrature technique that uses quintic B-spline as the basis functions for space integration. The derivatives are approximated using differential quadrature method. The weighting coefficients are obtained by semi-explicit algorithm. Five-band Thomas algorithm has been employed to solve the resultant algebraic system that can be reduced into a penta-diagonal matrix. Stability analysis of method has also been done. The accuracy of the proposed scheme is demonstrated by applying on three test problems. Theoretical attributes such as existence, uniqueness and regularity of Fisher-Kolmogorov equations are also conferred. The outcomes are depicted graphically to confirm accuracy of the findings and performance of this method and a comparative study is done with results available in the literature. The computed results are found to be in good agreement with the analytical solutions.
21 citations
TL;DR: In this article, the influence of the quintic nonlinear term on the ideal 1D pure cigar-like shape model for attractive and repulsive atom-atom interaction in Bose-Einstein condensates was explored.
Abstract: By means of a new variational method we report a direct solution for quintic and cubic-quintic nonlinear 1D Gross-Pitaeskii equations (GPE) in a harmonic confined potential. We explore the influence of the quintic nonlinear term on the ideal 1D pure cigar-like shape model for attractive and repulsive atom-atom interaction in Bose-Einstein condensates (BEC). Also, we offer a closed analytical expression to evaluate the error produced when solely the cubic nonlinear GPE is considered in the description of 1D BEC.
21 citations
TL;DR: In this article, the quintic nonlinear Schrodinger equa- tion on the circle was solved in a nonlinear nonlinear way. But it was not shown how to solve the nonlinear version of the problem.
Abstract: We construct solutions to the quintic nonlinear Schrodinger equa- tion on the circle i@tu + @ 2 xu = � j uj
20 citations
TL;DR: In this article, the authors obtained optical solitons and other solitary wave solutions for (2+1)-dimensional nonlinear Schrodinger equation (NLSE) with the aid of extended modified auxiliary equation mapping method, together with cubic-quintic-septic nonlinearity.
20 citations