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: In this paper, a neural network scheme based on quintic B-spline functions of optimality systems arising from linear parabolic optimal control problems is discussed, and the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to the optimal solution of the original problem.
Abstract: A neural network scheme based on quintic B-spline functions of optimality systems arising from linear parabolic optimal control problems is discussed. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to the optimal solution of the original problem. Theoretical and experimental results show the advantages of B-spline functions and demonstrate that the suggested scheme is able to efficiently solve constrained optimal control problems. The resulting scheme also shows that robustness with respect to changes of the value of $$
u $$
, the weight of the cost of the control, is sufficiently small.
6 citations
TL;DR: In this paper, the exact vortex solutions for topological charge S ≥ 1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential were constructed.
Abstract: Applying the similarity transformation, we construct the exact vortex solutions for topological charge S ≥ 1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S ≥ 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.
6 citations
TL;DR: In this article , a generalized nonlinear Schrödinger equation with pseudo-quintic nonlinearity and self-steepening effect is proposed to propagate ultrashort pulses at least a few tens of optical cycles in duration through a negative index material.
6 citations
TL;DR: This work uses piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction-diffusion equation, replacing it thus with a set of simple linear inhomogeneous differential equations, yielding an excellent approximation to the exact propagating front.
Abstract: We use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction-diffusion equation, replacing it thus with a set of simple linear inhomogeneous differential equations. The resulting analytic solution constitutes an excellent approximation to the exact propagating front, as is explicitly shown in the case of cubic and quintic nonlinearities, yielding also the correct value for the physically selected speed of the observable front. Such a piecewise linear emulation can be used for any nonlinearity, giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states, especially pushed fronts.
6 citations
TL;DR: Using the bifurcation theory and the method of detection function, it is obtained that this system exists at least 14 limit cycles with the distribution C 9 1 ⊃ [ C 1 1 + 2 ( C 3 2 ⊁ 2 C 1 2 ) ] .
6 citations