Showing papers on "Quintic function published in 2021"
98 citations
59 citations
TL;DR: In this article, the exact soliton solutions under the effect of cubic-quintic-septic nonlinearities for a 6-order (3 + 1 ) -dimensional nonlinear time-fractional Schrodinger equation with fourth-order and sixth-order dispersive terms were examined.
55 citations
TL;DR: In this article, the authors construct families of fundamental, dipole, and tripole solitons in the fractional Schrodinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos 2 x and sin 2 x, respectively.
Abstract: We construct families of fundamental, dipole, and tripole solitons in the fractional Schrodinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos 2 x and sin 2 x , respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the Levy index (LI) that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.
42 citations
TL;DR: In this article, the fundamental aim is to find the iterative solution for generalized quintic co-occurrence problems with respect to nonlinear phenomena associated with physical phenomena, which is a hot topic in the present era.
Abstract: The study of nonlinear phenomena associated with physical phenomena is a hot topic in the present era. The fundamental aim of this paper is to find the iterative solution for generalized quintic co...
39 citations
TL;DR: In this article, the authors examined three different recent computational schemes (extended simplest equation (ESE), modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel algorithms.
Abstract: This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel ...
32 citations
01 Jan 2021
TL;DR: In this paper, 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.
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.
30 citations
TL;DR: In this paper, the cubic-quintic nonlinear Schrodinger equation of up to three dimensions is considered and the cubic nonlinearity is thereby focusing while the quintic one is defocusing, ensuring global well-po...
Abstract: We consider the cubic-quintic nonlinear Schrodinger equation of up to three space dimensions. The cubic nonlinearity is thereby focusing while the quintic one is defocusing, ensuring global well-po...
28 citations
TL;DR: In this article, the authors prove the large data scattering for two models, i.e., the defocusing quintic nonlinear Schrodinger equation on R 2 × T and the def focusing cubic nonlinear Schrrodinger equations on R 3 × T.
24 citations
TL;DR: In this paper, a new transformation v = 4 ( ln f ) x x that can formulate a quintic linear equation and a pair of Hirota's bilinear equations for the (2 − 1)-dimensional Sawada-Kotera (2DSK) Eq. (2) is reported.
24 citations
TL;DR: In this article, the authors obtained optical solitons and other solitary wave solutions for (2+1)-dimensional nonlinear Schrodinger equation (NLSE) with the aid of extended modified auxiliary equation mapping method, together with cubic-quintic-septic nonlinearity.
TL;DR: In this article, the fractal cubic cubic quintic Duffing's equation analytical solution is obtained using the two-scale transform and elliptic functions, which is used to study wave wave.
Abstract: In this work, the fractal cubic–quintic Duffing’s equation analytical solution is obtained using the two-scale transform and elliptic functions. Then, the analytical solution is used to study wave ...
TL;DR: The Homotopy perturbation method is utilized to obtain an approximate solution with an artificial frequency of the given system, and various numerical solutions to initial–boundary value problems are deduced via a three-step finite difference scheme.
TL;DR: In this article, the gamma function method was used to solve the nonlinear cubic cubic-quintic Duffing oscillators with and witho(n) with the first time ever.
Abstract: In this article, the gamma function method, for the first time ever, is used to solve the nonlinear cubic-quintic Duffing oscillators. The nonlinear cubic-quintic Duffing oscillators with and witho...
TL;DR: In this article, the dromion-like excitations corresponding to intramolecular chain-like proteins are described by using cubic-quintic nonlinear Schrodinger equation (CQNSE) governing the dynamics of proteins.
Abstract: We investigate the dromion-like excitations corresponding to intramolecular chain-like proteins. In the present work, the dromion-like excitations are described by using cubic-quintic nonlinear Schrodinger equation (CQNSE) governing the dynamics of proteins and we analytically analyze the velocity (v) of dromion-like structure compared with velocity (
$$v_a$$
) of acoustical sound waves corresponding to the longitudinal vibrations of protein molecules. Our work is motivated by the effectiveness and powerful mathematical techniques such as modified extended tanh function method and sine–cosine function method for solving CQNSE to obtain dromion-like structures.
TL;DR: A trigonometric quintic B-spline method is proposed for the solution of a class of turning point singularly perturbed boundary value problems (SP-BVPs) whose solution exhibits either twin boundary layers near both endpoints of the interval of consideration or an interior layer near the turning point.
Abstract: A trigonometric quintic B-spline method is proposed for the solution of a class of turning point singularly perturbed boundary value problems (SP-BVPs) whose solution exhibits either twin boundary ...
TL;DR: A general framework for the path planning using quintic trigonometric Bezier curve with two shape parameters and continuity is proposed, expressing that when there are obstacles, predefined path can be adjusted by only using shape parameters without altering any obstacle.
Abstract: Path planning is one of the essential steps for autonomous ground vehicles or even wheeled mobile robots. This paper proposes a general framework for the path planning using quintic trigonometric Bezier curve with two shape parameters and $$C_{3}$$
continuity. We express that when there are obstacles, predefined path can be adjusted by only using shape parameters without altering any obstacle. Additionally, the velocity, lateral acceleration, longitudinal and lateral jerks of the predefined cubic and quintic Bezier, and cubic and quintic trigonometric Bezier paths are compared. Also, a path surface for autonomous ground vehicles can be generated using developable surfaces.
TL;DR: In this paper, the cubic-quintic nonlinear Schrodinger equation in two space dimensions was considered and X. Cheng established scattering for H1 data with mass strictly below that of the ground state.
Abstract: We consider the cubic-quintic nonlinear Schrodinger equation in two space dimensions. For this model, X. Cheng established scattering for H1 data with mass strictly below that of the ground state f...
TL;DR: In this article, the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds was obtained.
Abstract: We use numerical methods to obtain moduli-dependent Calabi-Yau metrics, and from them, the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their K\"ahler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods, and we compare the results. Finally, we fit the moduli dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order 1, as suggested by the swampland distance conjecture. We also observe level crossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations.
TL;DR: By using the quintic B-spline collocation method, n -dimensional stochastic Ito-Volterra integral equation can be reduced to a linear or nonlinear system of algebraic equations.
TL;DR: The Galerkin method, based on quintic B-spline function as the shape and weight functions is described for the numerical solution of the second order coupled nonlinear Schrodinger equations.
TL;DR: This study investigates the use of planar Pythagorean-hodograph (PH) curves as polynomial approximants to monotone clothoid segments, based on geometric Hermite interpolation of end points, tangents, and curvatures, and precise matching of the clothoid segment arc length.
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TL;DR: The number of polynomials that are irreducible with integer coefficients in the Galois group is O(H 2.91 ) as mentioned in this paper, which is the same as the number of quintic polynomial solvable by radicals.
Abstract: How often is a quintic polynomial solvable by radicals? We establish that the number of such polynomials, monic and irreducible with integer coefficients in $[-H,H]$, is $O(H^{3.91})$. More generally, we show that if $n \ge 3$ and $n
otin \{ 7, 8, 10 \}$ then there are $O(H^{n-1.017})$ monic, irreducible polynomials of degree $n$ with integer coefficients in $[-H,H]$ and Galois group not containing $A_n$. Save for the alternating group and degrees $7,8,10$, this establishes a 1936 conjecture of van der Waerden.
TL;DR: In this paper, the effects of filter and linear dissipation parameters on explosion excitation and wave amplitude modulation were studied, and exact solutions of discrete conformable fractional complex cubic cubic cubic-quintic Ginzburg-Landau model possessing non-local quintic term were derived.
TL;DR: A general theory about the existence and the uniqueness of the optimal approximant is presented and a rigorous analysis is done for some special cases for which the degree of the polynomial curve and the order of the geometric smoothness differ by two.
TL;DR: A numerical scheme for the singular Emden–Fowler problem using quintic B-spline is investigated and the singularity of the problem is eliminated according to Lopita's law and a new high-precision solution is obtained through a linear combination of the original solutions.
Abstract: In this paper, we investigate a numerical scheme for the singular Emden–Fowler problem using quintic B-spline. We eliminate the singularity of the problem according to Lopita's law and obtain a new...
TL;DR: In this article, the persistence of finite and infinite dimensional invariant tori is proved in the original elliptic variables without passing to action-angle ones, and the persistence result is given through a rather abstract counterterm theorem.
TL;DR: In this paper, a set of conditions enabling a polynomial system of ordinary differential equations in the plane to have invariant algebraic curves is presented, which are necessary and sufficient.
Abstract: We present a set of conditions enabling a polynomial system of ordinary differential equations in the plane to have invariant algebraic curves. These conditions are necessary and sufficient. Our main tools include factorizations over the field of Puiseux series near infinity of bivariate polynomials generating invariant algebraic curves. The set of conditions can be algorithmically verified. This fact gives rise to a method, which is able not only to find some irreducible invariant algebraic curves, but also to perform their classification. We study in details the problem of classifying invariant algebraic curves in the most difficult case: we consider differential systems with infinite number of trajectories passing through infinity. As an example, we find necessary and sufficient conditions such that a general polynomial Lienard differential system has invariant algebraic curves. We present a set of all irreducible invariant algebraic curves for quintic Lienard differential systems with a linear damping function. It is supposed in scientific literature that the degrees of their irreducible invariant algebraic curves are bounded by 6. While we derive irreducible invariant algebraic curves of degree 9.