Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the quintic nonlinear Schrodinger equation (NLS) on the circle was considered and it was shown that there exist solutions corresponding to an initial datum built on four Fourier modes which form a resonant set, which have a nontrivial dynamic that involves periodic energy exchanges between the modes initially excited.
Abstract: We consider the quintic nonlinear Schrodinger equation (NLS) on the circle i ∂ t u + ∂ x 2 u = ± ν | u | 4 u , ν ≪ 1 , x ∈ S 1 , t ∈ R . We prove that there exist solutions corresponding to an initial datum built on four Fourier modes which form a resonant set (see Definition 1.1), which have a nontrivial dynamic that involves periodic energy exchanges between the modes initially excited. It is noticeable that this nonlinear phenomenon does not depend on the choice of the resonant set. The dynamical result is obtained by calculating a resonant normal form up to order 10 of the Hamiltonian of the quintic NLS and then by isolating an effective term of order 6. Notice that this phenomenon cannot occur in the cubic NLS case for which the amplitudes of the Fourier modes are almost actions, i.e. they are almost constant.
46 citations
TL;DR: A new fourth order method using quintic polynomials for the smooth approximation of the two point boundary value problems involving second order differential equations lacking the first derivative, which outperforms the well-known fourth order Noumerov's finite difference scheme.
Abstract: A new fourth order method using quintic polynomials is designed in this paper for the smooth approximation of the two point boundary value problems involving second order differential equations lacking the first derivative. The present method enables us to approximate the unknown function as well as its derivative at every point of the range of integration and thus it has obvious advantages over other discrete numerical methods. Our present method outperforms the well-known fourth order Noumerov's finite difference scheme. The convergence of the method is briefly outlined using matrix algebra and two numerical illustrations are provided to demonstrate the practical suitability of our approach.
46 citations
TL;DR: In this article, the effects of quintic nonlinearity on ultrashort optical pulse propagation in non-Kerr media were studied by virtue of the Darboux transformation (DT) and symbolic computation.
46 citations
TL;DR: In this article, the authors considered the problem of large-data scattering for the quintic nonlinear Schrodinger equation on R × T2 and proposed a large-scale profile that controls the asymptotic behavior of the solutions.
Abstract: We consider the problem of large-data scattering for the quintic nonlinear Schrodinger equation on R × T2. This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a “large-scale profile”) that controls the asymptotic behavior of the solutions. © 2014 Wiley Periodicals, Inc.
46 citations
TL;DR: In this article, the authors constructed the new exact solutions of a nonlinear evolution equation that appears in mathematical physics, specifically complex cubic-quintic Ginzburg-Landau equation by the first integral method.
46 citations