The aim of this study is to obtain numerical solutions the modified Fornberg Whitham equation via collocation finite element method combined with operator splitting method. used convert original into two sub equations including linear and nonlinear part as a slight modification idea. After progress, reduce algebraic systems. For purpose, quintic B-spline base functions are polynomial approximat...

Abstract: The aim of this paper is to provide a realistic stochastic trajectory generation method for unmanned aerial vehicles that offers a tool for the emulation of trajectories in typical flight scenarios. Three scenarios are defined in this paper. The trajectories for these scenarios are implemented with quintic B-splines that grant smoothness in the second-order derivatives of Euler angles...

We study, analytically, the discrete complex cubic–quintic Ginzburg–Landau (dCCQGL) equation with a non-local quintic term. We find a set of exact solutions which includes, as particular cases, bright and dark soliton solutions, constant magnitude solutions with phase shifts, periodic solutions in terms of elliptic Jacobi functions in general forms, and various particular periodic solutions.  ...

The modulation instability of the one-dimensional cubic-quintic complex Ginzburg-Landau equation with fouth-order dispersion and gain terms, a. k. a., the quintic complex Swift-Hohenberg equation, is investgated. The effects of the fourth-order terms to the modulational instability is studied. We numerically investigate the dynamics of the modulational instability in the presence of the fourtho...

We have numerically calculated the resonance curve and the region of existence of high-energy dissipative solitons in systems governed by the complex cubic-quintic Ginzburg-Landau equation. The calculations are carried out for negative reactive quintic nonlinearity. This choice allows the resonance curve to be continued into the region of positive net dispersion, thus showing that high-energy p...

Walton & Meek [13] obtained fair G Pythagorean hodograph (PH) quintic transition Sand C-shaped curves connecting two circles. It was shown that an S-shaped curve has no curvature extremum and a Cshaped curve has a single curvature extremum. We simplified and completed their analysis. A family of fair PH quintic transition curves between two circles has been derived. We presented an algorithm wi...

The purpose of this paper is to study some properties of the Newton maps associated to real quintic polynomials. First using the Tschirnhaus transformation, we reduce the study of Newton’s method for general quintic polynomials to the case f(x) = x − c x + 1. Then we use symbolic dynamics to consider this last case and construct a kneading sequences tree for Newton maps. Finally, we prove that ...