The research status of industrial robot trajectory planning is discussed in detail, and the applicable occasions cubic polynomial interpolation, quintic B-spline curve, mixed interpolation other methods commonly used basic are comprehensively analyzed. At same time, various optimal for robots reviewed. advantages disadvantages compared important direction prospected.

By means of the coupled amplitude-phase method we find analytical dark solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short (femtosecond) optical soliton propagation in non-Kerr media. The dark solitary wave solution exists even for the coefficients of quintic terms much larger than...

In this paper we present the soliton dynamics in a two port fiber nonlinear directional coupler with periodically modulated dispersion and coupling constant dispersion that arose due to the intermodal dispersion between symmetric and antisymmetric modes of the coupler. The fiber material possessed cubic quintic nonlinearity. The influences of the coupling constant dispersion, periodically modul...

Small quantum fluctuations in solitons described by the cubic–quintic nonlinear Schrödinger equation (CQNLSE) are studied within the linear approximation. The cases of both self-defocusing and self-focusing quintic terms are considered (in the latter case, the solitons may be effectively stable, despite the possibility of collapse). The numerically implemented back-propagation method is used to...

We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schrodinger equation, which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagati...

We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor’s algorithm for spli...

In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, cubic NLS, and 2d quintic NLS (nonlinear Schrödinger equations).

In this article, a fourth order quintic spline method has been developed to obtain numerical solutions for second order boundary value problems with Dirichlet boundary conditions. The developments of the quintic spline method and convergence analysis were presented. Three test problems have been considered for comparison purposes. The numerical results showed that the quintic spline method is m...

We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer’s quintic polynomials.