Showing papers on "Quintic function published in 2019"
TL;DR: In this paper, the authors applied F-expansion algorithm to obtain highly dispersive optical solitons with cubic-quintic-septic nonlinearity, and their respective existence criteria are also indicated.
107 citations
TL;DR: In this paper, the Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic three-folds were studied.
Abstract: We study the Clifford type inequality for a particular type of curves $$C_{2,2,5}$$
, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov–Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macri, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in $$\mathbf {P}^4_{\mathbb {C}}$$
.
65 citations
TL;DR: In this paper, three-dimensional analytical optical soliton solutions are found based on some high-order nonlinear Schrodinger equations, and the stability of solitons in the cubic-quintic nonlinear case is better than that in cubic nonlinear cases, but worse than the cubic quintic-septimal case.
Abstract: Under parity-time symmetric potentials, different-order nonlinearities such as cubic, quintic and septimal nonlinearities, altogether with their combinations and second-order and fourth-order dispersions/diffractions are simultaneously considered to form three-dimensional optical solitons. Based on some high-order nonlinear Schrodinger equations, three-dimensional analytical optical soliton solutions are found. In the defocusing cubic nonlinear case, three-dimensional optical soliton without fourth-order diffraction/dispersion is stable than that with fourth-order diffraction/dispersion. However, in the defocusing cubic and focusing quintic nonlinear case, the stability situation of soliton is just on the contrary. Among all combinations of nonlinearity, the stability of three-dimensional optical soliton in the cubic-quintic nonlinear case is better than that in the cubic nonlinear case, but worse than that in the cubic-quintic-septimal nonlinear case. In the quintic-septimal nonlinear case, three-dimensional optical soliton is unstable and will collapse ultimately.
64 citations
TL;DR: Using the asymmetric method, the analytic one-soliton solution of the CCQGLE is obtained for the first time and it is shown that the transmission of the soliton is controlled by changing the values of related parameters.
57 citations
TL;DR: In this article, a quintic time-dependent coefficient derivative nonlinear Schrodinger equation for certain hydrodynamic wave packets or a medium with the negative refractive index is investigated, and a gauge transformation is found to obtain the equivalent form of the equation.
Abstract: Under investigation in this paper is a quintic time-dependent coefficient derivative nonlinear Schrodinger equation for certain hydrodynamic wave packets or a medium with the negative refractive index. A gauge transformation is found to obtain the equivalent form of the equation. With respect to the wave envelope for the free water surface displacement or envelope of the electric field, Painleve integrable condition, different from that in the existing literature, is derived, with which the bilinear forms and N-soliton solutions are constructed. Asymptotic analysis illustrates that the interactions between the bright and bound solitons as well as between the bright solitons and Kuznetsov–Ma breathers are elastic with certain conditions, while some other interactions are inelastic under other conditions. Propagation paths and velocities for the solitons are both affected by the dispersion coefficient function when the relations among the coefficients are linear, or affected by the dispersion coefficient, self-steepening coefficient and cubic nonlinearity functions when the relations among the coefficients are nonlinear. Under different conditions, bell-shaped solitons can evolve into the bound solitons or Kuznetsov–Ma breathers, respectively. Interactions between the bright and parabolic (or hyperbolic) solitons are related to the dispersion coefficient, self-steepening coefficient and cubic nonlinearity functions. Compression effect on the propagation paths of the solitons, caused by the dispersion coefficient, is observed.
55 citations
TL;DR: In this paper, an external periodic potential (linear lattice) was incorporated into the cubic-quintic model and extended it to the space-fractional scenario that begins to surface in very recent years, therefore obtaining the cubic or purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein.
Abstract: Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic-quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrodinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years---the nonlinear fractional Schrodinger equation (NLFSE), therefore obtaining the cubic-quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov-Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic-quintic nonlinear terms.
53 citations
TL;DR: The extended Jacobi's elliptic function scheme is implemented to retrieve bright, dark and singular highly dispersive optical solitons that is studied in cubic-quintic-septic nonlinear medium.
51 citations
TL;DR: In this paper, the authors obtained optical soliton solutions for non-Kerr law nonlinear Schrodinger equation (NLSE) with third order (3OD) and fourth order dispersions (4OD).
37 citations
TL;DR: In this article, an external periodic potential (linear lattice) was incorporated into the cubic-quintic model and extended to the space-fractional scenario, thus obtaining the cubic or purely quintic NLFSE.
Abstract: Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic–quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrodinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years—the nonlinear fractional Schrodinger equation (NLFSE), therefore obtaining the cubic–quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov–Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic–quintic nonlinear terms.
33 citations
10 Dec 2019
TL;DR: In this paper, the cubic-quintic Ginzburg-Landau equation was derived as a modulation equation for the stochastic Swift-Hohenberg equation with cubic quintic nonlinearity on an unbounded domain near a change of stability.
Abstract: The purpose of this paper is to rigorously derive the cubic–quintic Ginzburg–Landau equation as a modulation equation for the stochastic Swift–Hohenberg equation with cubic–quintic nonlinearity on an unbounded domain near a change of stability, where a band of dominant pattern is changing stability. Also, we show the influence of degenerate additive noise on the stabilization of the modulation equation.
33 citations
TL;DR: In this article, Hosseinia et al. presented the High-Order Dispersive Cubic-Quintic Schrödinger Equation and its Exact Solutions.
Abstract: High-Order Dispersive Cubic-Quintic Schrödinger Equation and Its Exact Solutions K. Hosseinia,∗, R. Ansari, F. Samadani, A. Zabihi, A. Shafaroody and M. Mirzazadeh Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran Department of Mechanical Engineering, Ahrar Institute of Technology and Higher Education, Rasht, Iran Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157 Rudsar-Vajargah, Iran
TL;DR: In this paper, the authors investigated the possibility of spontaneous scalarization of static, spherically symmetric, and asymptotically flat black holes (BHs) in the Horndeski theory.
Abstract: We investigate the possibility of spontaneous scalarization of static, spherically symmetric, and asymptotically flat black holes (BHs) in the Horndeski theory. Spontaneous scalarization of BHs is a phenomenon that the scalar field spontaneously obtains a nontrivial profile in the vicinity of the event horizon via the nonminimal couplings and eventually the BH possesses a scalar charge. In the theory in which spontaneous scalarization takes place, the Schwarzschild solution with a trivial profile of the scalar field exhibits a tachyonic instability in the vicinity of the event horizon, and evolves into a hairy BH solution. Our analysis will extend the previous studies about the Einstein-scalar-Gauss-Bonnet (GB) theory to other classes of the Horndeski theory. First, we clarify the conditions for the existence of the vanishing scalar field solution ϕ=0 on top of the Schwarzschild spacetime, and we apply them to each individual generalized Galileon coupling. For each coupling, we choose the coupling function with minimal power of ϕ and X≔-(1/2)gμν∂μϕ∂νϕ that satisfies the above condition, which leaves nonzero and finite imprints in the radial perturbation of the scalar field. Second, we investigate the radial perturbation of the scalar field about the ϕ=0 solution on top of the Schwarzschild spacetime. While each individual generalized Galileon coupling except for a generalized quartic coupling does not satisfy the hyperbolicity condition or realize a tachyonic instability of the Schwarzschild spacetime by itself, a generalized quartic coupling can realize it in the intermediate length scales outside the event horizon. Finally, we investigate a model with generalized quartic and quintic Galileon couplings, which includes the Einstein-scalar-GB theory as the special case, and show that as one increases the relative contribution of the generalized quartic Galileon term the effective potential for the radial perturbation develops a negative region in the vicinity of the event horizon without violation of hyperbolicity, leading to a pure imaginary mode(s) and hence a tachyonic instability of the Schwarzschild solution.
TL;DR: A comprehensive analysis of the existence of solutions in the case of spatial PH quintics with end derivatives of equal magnitude is presented, establishing that a two–parameter family of interpolants exists for any prescribed end points, end tangents, and total arc length.
TL;DR: In this paper, the supratransmission phenomenon in the discrete nonlinear Schrodinger equation with the cubic-quintic nonlinearity was numerically analyzed, and it was shown that the lattice induces the generation of the train of dark solitons carried by a traveling kink and the traveling Kink for chosen driving amplitude.
Abstract: We numerically analyzed the supratransmission phenomenon in the discrete nonlinear Schrodinger equation with the cubic–quintic nonlinearity. It has been reported that the homoclinic nonlinear band-gap threshold matches very well with the model. In the case of the cooperation between the nonlinearities (self-focusing cubic and quintic terms), the train of discrete band-gap waves overcomes the potential barrier of the first sites before merging or rebounding. In the case of competing self-focusing cubic and defocusing quintic nonlinearities, it is found that the lattice induces the generation of the train of dark solitons carried by a traveling kink and the traveling kink for chosen driving amplitude.
TL;DR: In this paper, two B-spline collocation methods for a class of nonlinear singular Lane-Emden type equations which describe several phenomena in theoretical physics and astrophysics are described.
TL;DR: In this paper, it was shown that a curve of degree dk on a very general surface of degree n ≥ 5 in P 3 has geometric genus at least d k (d − 5 ) + k 2 + 1.
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.
01 Mar 2019
TL;DR: In this article, Chen et al. define a formal Gromov-Witten theory of the quintic via localization on new moduli spaces and prove the existence of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model physics.
Abstract: We define a formal Gromov–Witten theory of the quintic threefold via localization on $${\mathbb {P}}^4$$
. Our main result is a direct geometric proof of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model physics for the true Gromov–Witten theory of the quintic threefold. The results suggest that the formal quintic and the true quintic theories should be related by transformations which respect the holomorphic anomaly equations. Such a relationship has been recently found by Q. Chen, S. Guo, F. Janda, and Y. Ruan via the geometry of new moduli spaces.
TL;DR: A constructive approach to solve the first-order Hermite interpolation problem in ℝ3 is provided and Comparisons with the polynomial case are illustrated to point out the greater flexibility of ATPH curves with respect to polynometric PH curves.
Abstract: We introduce a new class of Pythagorean-Hodograph (PH) space curves - called Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) space curves - that are defined over a six-dimensional space mixing algebraic and trigonometric polynomials. After providing a general definition for this new class of curves, their quaternion representation is introduced and the fundamental properties are discussed. Then, as previously done with their quintic polynomial counterpart, a constructive approach to solve the first-order Hermite interpolation problem in ℝ3 is provided. Comparisons with the polynomial case are illustrated to point out the greater flexibility of ATPH curves with respect to polynomial PH curves.
TL;DR: In this paper, the parametrized post-Newtonian-Vainshteinian (PPNV) formalism is applied to the quartic and quintic Galileon theories for the first time.
Abstract: Recently, an extension to the parametrized post-Newtonian (PPN) formalism has been proposed. This formalism, the parametrized post-Newtonian-Vainshteinian (PPNV) formalism, is well suited to theories which exhibit Vainshtein screening of scalar fields. In this paper we apply the PPNV formalism to the quartic and quintic Galileon theories for the first time. As simple generalizations of standard scalar-tensor field theories they are important guides for the generalization of parametrized approaches to the effects of gravity beyond general relativity. In the quartic case, we find new PPNV potentials for both screened and unscreened regions of spacetime, showing that in principle these theories can be tested. In the quintic case we show that Vainshtein screening does not occur to Newtonian order, meaning that the theory behaves as Brans-Dicke to this order, and we discuss possible higher order effects.
TL;DR: In this article, two resonant Hamiltonian systems on the phase space L2(R→C) were studied: the quintic one-dimensional continuous resonant equation and a cubic resonant system.
Abstract: We study two resonant Hamiltonian systems on the phase space L2(R→C): the quintic one-dimensional continuous resonant equation, and a cubic resonant system that has appeared in the literatu...
TL;DR: In this article, the authors used tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds.
Abstract: We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds.
We apply this construction to the tropical curves obtained from the 2875 lines on the quintic Calabi-Yau threefold.
Each admissible tropical curve gives a Lagrangian rational homology sphere in the corresponding mirror quintic threefold and disjoint curves give pairwise homologous but non-Hamiltonian isotopic Lagrangians.
We check in an example that $>300$ mutually disjoint curves (and hence Lagrangians) arise.
We show that the weight of each of these Lagrangians equals to the multiplicity of the corresponding tropical curve.
01 Jan 2019
TL;DR: In this paper, the quintic nonlinear Schrodinger equation on ℝ d with randomized initial data below the critical regularity H ( d − 1 ) ∕ 2 for d ≥ 3 was studied.
Abstract: This paper studies the quintic nonlinear Schrodinger equation on ℝ d with randomized initial data below the critical regularity H ( d − 1 ) ∕ 2 for d ≥ 3 . The main result is a proof of almost sure local well-posedness given a Wiener randomization of the data in H s for s ∈ ( 1 2 ( d − 2 ) , 1 2 ( d − 1 ) ) . The argument further develops the techniques introduced in the work of A. Benyi, T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a condition for almost sure global well-posedness.
TL;DR: In this paper, the authors used Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives, and the method therefore guarantees that thermodynamic identities are obeyed even between mesh points.
Abstract: Aims . We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation.Methods . We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines.Results . The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum lgP difference lies in the range from 10−9 to 10−4 , and Γ1 difference varies from 10−9 to 10−3 . Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at T ∼ 1.5 × 103 −105 K. The best precision is achieved at higher temperatures, T > 105 K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.
TL;DR: In this article, a smoothing type property for solutions of the 1d quintic Schrodinger equation was proposed and a family of natural Gaussian measures are quasi-invariant under the flow of this equation.
Abstract: We prove a new smoothing type property for solutions of the 1d quintic Schrodinger equation. As a consequence, we prove that a family of natural Gaussian measures are quasi-invariant under the flow of this equation. In the defocusing case, we prove global in time quasi-invariance while in the focusing case we only get local in time quasi-invariance because of a blow-up obstruction. Our results extend as well to generic odd power nonlinearities.
TL;DR: In this paper, the nonlinear Bratu type equation is numerically solved via quintic B-spline method and it is shown that the proposed technique has fourth order convergence.
Abstract: In this paper, the nonlinear Bratu type equation is numerically solved via quintic B-spline method. It is shown that the proposed technique has fourth order convergence. The efficiency and ...
04 Jun 2019
TL;DR: In this article, the stability of the Hyers-Ulam-Rassias stability of general quintic functional equations and the general sextic functional equation was investigated, which is a generalization of many functional equations such as the additive function equation and quadratic function equation.
Abstract: The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation.
TL;DR: This paper is concerned with the numerical solution of the nonlinear Schrodinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain.
Abstract: This paper is concerned with the numerical solution of the nonlinear Schrodinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 , I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.