Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

Abstract: The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”. A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrodinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.

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

Strong Langmuir turbulence dynamics through the trigonometric quintic and exponential B-spline schemes

Abstract: In this manuscript, two recent numerical schemes (the trigonometric quintic and exponential cubic B-spline schemes) are employed for evaluating the approximate solutions of the nonlinear Klein-Gordon-Zakharov model. This model describes the interaction between the Langmuir wave and the ion-acoustic wave in a high-frequency plasma. The initial and boundary conditions are constructed via a novel general computational scheme. [ 1 ] has used five different numerical schemes, such as the Adomian decomposition method, Elkalla-expansion method, three-member of the well-known cubic B-spline schemes. Consequently, the comparison between our solutions and that have been given in [ 1 ], shows the accuracy of seven recent numerical schemes along with the considered model. The obtained numerical solutions are sketched in two dimensional and column distribution to explain the matching between the computational and numerical simulation. The novelty, originality, and accuracy of this research paper are explained by comparing the obtained numerical solutions with the previously obtained solutions.

Calabi-Yau manifolds over finite fields. 2.

Abstract: We study ζ-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The ζ-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to ‘see’ these curves in the geometry of the quintic. Having these ζ-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the ζ-functions is suggested by an application of the Weil conjec- tures to Calabi–Yau threefolds: the ζ-functions are rational functions and the degrees of the numerators and denominators are exchanged between the ζ-functions for the manifold and its mirror. It is clear nevertheless that the ζ-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a ‘quantum modification’ of the ζ-function that restores the symmetry between the Kahler and complex structure param- eters. We note that the ζ-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion.