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...

Surface offset is one of the most useful operations in Computer Aided Geometric Design (CAGD). However, an implementation of this operator is not trivial primarily because the offset surface, in general, does not have the same representation as the original surface. Hence, it is dif®cult or impossible to represent an exact offset in a system with limited surface forms. For this reason, some CAG...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions has been developed to solve a general seventh order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and ...

Conventional tool paths for computer numericalcontrolled (CNC) machine tools or NC positioning systems are mainly composed of linear motion segments, or the socalled G1 commands. This approach exhibits serious limitations in terms of achieving the desired part of geometry and productivity in high-speed machining. Velocity and acceleration discontinuities occur at the junction points of consecut...

In this paper, a finite element method involving Petrov-Galerkin method with quartic B-splines as basic functions and quintic B-splines as weight functions has been developed to solve a general sixth order boundary value problem with a particular case of boundary conditions. The basic functions are redefined into a new set of basic functions which vanish on the boundary where the Dirichlet and ...

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...

Cycle time minimization is one of the major goals to achieve in manufacturing. Maximizing feedrate direct solution; however, physical motions need be under specified motion limits avoid high-frequency vibration, causing machining error. In this paper, a time-optimal scheduling approach with corner smoothing for 5-axis G1 toolpaths presented machining. One key feature proposed method describe or...

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...