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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 article, the authors proposed an efficient generalization of the trial equation method introduced recently by Liu [Appl. Math. Comput. 217 (2011) 5866] to construct exact chirped traveling wave solutions of complex differential equations with variable coefficients.
Abstract: In this work, we propose an efficient generalization of the trial equation method introduced recently by Liu [Appl. Math. Comput. 217 (2011) 5866] to construct exact chirped traveling wave solutions of complex differential equations with variable coefficients. The effectiveness of the proposed method has been tested by applying it successfully to the quintic derivative nonlinear Schrodinger equation with variable coefficients. As a result, a class of chirped soliton-like solutions including bright and kink solitons is derived for the first time. Compared with previous work of Liu in which unchirped solutions were given, we obtain exact chirped solutions which have nontrivial phase that varies as a function of the wave intensity. These localized structures characteristically exist due to a balance among the group-velocity dispersion, self-steepening and competing cubic-quintic nonlinearity. Parametric conditions for the existence of envelope solutions with nonlinear chirp are also presented. It is shown th...
14 citations
TL;DR: In this paper, a new quintic discrete nonlinear Schrodinger (QDNLS) equation is studied and exact localized solutions for integrable cases are presented for certain sets of parameters.
Abstract: We study a new quintic discrete nonlinear Schr\"odinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form $\phi_{n+1}+\phi_{n-1}=F(\phi_n)$. Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.
14 citations
TL;DR: In this paper, the existence of a local analytic first integral for a family of quintic systems with homogeneous nonlinearities has been shown in polynomial families of Lotka-Volterra systems.
14 citations
TL;DR: This work rigorously proves that the PH interpolant it selects doesn’t depend on the unit pure vector chosen for representing its hodograph in quaternion form, and evaluates the corresponding interpolation scheme from a theoretical point of view, proving with the help of symbolic computation that it has fourth approximation order.
14 citations
01 Jun 2019
TL;DR: In this article, the stochastic nonlinear Schrodinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative forcing were considered and global well-posedness in the energy and scaling-subcritical Sobolev spaces was shown.
Abstract: We consider the stochastic nonlinear Schrodinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in $$L^2(\mathbb {T})$$
. As for other power-type nonlinearities, namely (i) (super)quintic when $$d = 1$$
and (ii) (super)cubic when $$d \ge 2$$
, we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems.
14 citations