We consider the following nonlinear Schrödinger equation of derivative type: 1 $$\begin{aligned} i \partial _t u + _x^2 +i |u|^{2} _x +b|u|^4u=0 , \quad (t,x) \in {{\mathbb {R}}}\times {R}}}, \ b {R}}}. \end{aligned}$$ If $$b=0$$ this is a gauge equivalent form well-known (DNLS) equation. The soliton profile DNLS satisfies certain double power elliptic with cubic–quintic nonlinearities. quintic...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...

A method to generate a quintic B-spline curve which passes through given points is described. In this case, there are four more equations than there are control point positions. Two methods have been developed to compensate for the difference between the number of unknowns and that of the equations. These are assuming that the curvatures at both ends of the curve are zero, and assigning four gr...

In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular perturbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spl...

We present an e cient algorithm to construct C smooth meshes of quintic A-patches that interpolate or approximate the vertices of a given triangulated polyhedron P. An A-patch is a smooth and functional zero-contour patch of a trivariate polynomial in Bernstein-B ezier (BB) form de ned within a tetrahedron. A simplicial hull is constructed based on P. A quintic A-patch is then constructed withi...

In this paper a numerical method is proposed to approximate the solution of the nonlinear general Rosenau-RLW Equation. The method is based on collocation of quintic B-splines over finite elements so that we have continuity of the dependent variable and its first four derivatives throughout the solution range. We apply quintic B-splines for spatial variable and derivatives which produce a syste...

The limit cycle bifurcations of a Z2 equivariant quintic planar Hamiltonian vector field under Z2 equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.

I USE the term covariants to include invariants, and I write particularly concerning lists of covariants (groundforms) of the binary quintic and sextic, those of quantics of lower degree being few and well known. When the weight of a covariant is spoken of in this article, it must be understood to mean the weight of its first term or "source." The symbol 5ft will denote that covariant of the qu...