Showing papers on "Quintic function published in 2009"
TL;DR: In this article, a new approach for solving accurate approximate analytical higher-order solutions for strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force is presented.
111 citations
TL;DR: In this paper, the authors explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau three-fold.
Abstract: We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau three- folds. The domainwall tension is identified with a Poincare normal func- tion — a transversal holomorphic section of the Griffiths intermediate Jacobian — via the Abel-Jacobi map. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.
98 citations
TL;DR: It is shown how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential and the cubic and quintic nonlinearities.
Abstract: This work deals with soliton solutions of the nonlinear Schr\"odinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent paper [J. Belmonte-Beitia et al., Phys. Rev. Lett. 100, 164102 (2008)], and we solve the equation in the presence of a linear background and cubic and quintic interactions which are modulated in space and time. As a result, we show how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential and the cubic and quintic nonlinearities.
97 citations
TL;DR: In this article, the generalized Ulam-Hyer stability of the mixed type cubic and quartic functional equation in quasi-Banach spaces was obtained. But the general solution was not given.
Abstract: We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation in quasi-Banach spaces.
82 citations
TL;DR: In this paper, a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced, which is valid for all fraction values α ⩾ 1, the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time.
80 citations
TL;DR: In this paper, by means of similarity transformations, the quintic nonlinear Schrodinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates was constructed.
71 citations
TL;DR: In this article, the authors present an algorithm able to provide in closed form all those travelling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational.
Abstract: In order to flnd analytically the travelling waves of partially integrable au- tonomous nonlinear partial difierential equations, many methods have been pro- posed over the ages: \projective Riccati method", \tanh-method", \exponential method", \Jacobi expansion method",
ew ...", etc. The common default to all these \truncation methods" is to only provide some solutions, not all of them. By implementing three classical results of Briot, Bouquet and Poincare, we present an algorithm able to provide in closed form all those travelling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational. Our examples here include the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.
64 citations
TL;DR: In this paper, the existence, stability, and mobility of fundamental discrete solitons in two-and three-dimensional nonlinear Schrodinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities were investigated.
63 citations
TL;DR: In this paper, the authors present an algorithm able to find all traveling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational.
Abstract: In order to find analytically the travelling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: "projective Riccati method", "tanh-method", "exponential method", "Jacobi expansion method", "new ...", etc. The common default to all these "truncation methods" is to only provide some solutions, not all of them. By implementing three classical results of Briot, Bouquet and Poincare', we present an algorithm able to provide in closed form \textit{all} those travellingz waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational. Our examples here include the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.
61 citations
TL;DR: In this article, the cubic-quintic nonlinear Schrodinger equation with potentials and nonlinearities depending on both time and spatial coordinates was constructed by means of similarity transformations.
Abstract: In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic–quintic nonlinear Schrodinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose–Einstein condensates and nonlinear optics.
59 citations
TL;DR: Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%.
Abstract: In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtained using the Homotopy Analysis Method (HAM) and Homotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%.
TL;DR: In this paper, a radially symmetric blow up mechanism with L 2 concentration along the unit sphere of RN was shown to be stable in the presence of a log-log type singularity.
Abstract: We consider the quintic nonlinear Schr odinger equation in dimension N ≥ 3. This problem is energy critical in dimension N = 3 and energy super critical for N ≥ 4. We prove the existence of a radially symmetric blow up mechanism with L2 concentration along the unit sphere of RN . This singularity formation is moreover stable by smooth and radially symmetric perturbation of the initial data. This result extends the result obtained for N = 2 in [29] and is the first result of description of a singularity formation in the energy supercritical class for (NLS) type problems. Our main tool is the proof of the propagation of regularity outside the blow up sphere in the presence a so-called log-log type singularity.
TL;DR: The principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized and the solution of Cubic and Quartic Equations is presented.
Abstract: Summary. In this article, the principal n-th root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coecients are also presented [5].
TL;DR: In this article, a new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial.
TL;DR: In this paper, rank 2 arithmetically Cohen-Macaulay vector bundles on a general quintic hypersurface of the three-dimensional projective space are classified, and the rank 2 vector bundles are shown to be stable.
Abstract: Rank 2 arithmetically Cohen-Macaulay vector bundles on a general quintic hypersurface of the three-dimensional projective space are classified (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
TL;DR: A computational comparison study of quadratic, cubic, quartic and quintic splines for solving the modified regularized long wave (MRLW) equation shows that results corresponding to higher order splines are more accurate than those corresponding to lower ordersplines.
TL;DR: In this paper, the collocation method using quintic B-spline is derived for solving the complex modified Korteweg-de Vries (CMKdV) problem.
TL;DR: The existence of non-degenerate RRMF quintics is newly demonstrated through a constructive process, involving simple algebraic constraints on the coefficients of two quadratic complex polynomials that are sufficient and necessary for any PH quintic to admit a rational rotation-minimizing frame.
TL;DR: Computational results indicate that function-value-based cubic L"1 splines preserve shape well for all situations tested except the one in which an ''S-curve'' occurs when a flatter representation might be expected.
TL;DR: A survey of spline techniques for boundary value problems in ODEs can be found in this article, where the authors discuss the summary of the articles between 2000 and 2007 based on cubic, quintic, and sextic splines.
Abstract: In the present paper we describe a survey on recent spline techniques for solving boundary value problems in ordinary differential equations. Here we discuss the summary of the articles between 2000 and 2007 based on cubic, quintic, and sextic splines. Comparisons of methods with our own critical comments as remarks have been included.
TL;DR: A simple method to select the best quintic interpolant among all possible solutions is suggested and a full characterization of helical polynomial curves of any degree and a simple way to construct them are given.
Abstract: We give a full characterization of helical polynomial curves of any degree and a simple way to construct them Existing results about Hermite interpolation are revisited A simple method to select the best quintic interpolant among all possible solutions is suggested
TL;DR: It is shown that the quintic term with the self-defocusing/focusing sign makes the resonant response of the 2-soliton to the NLM essentially broader in terms of the frequency.
Abstract: We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schrodinger equation, which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagation in media with cubic-quintic optical nonlinearities and periodic alternation of linear loss and gain and to Bose–Einstein condensates, with the self-focusing quintic term accounting for the weak deviation of the dynamics from one dimensionality, while the NLM can be induced by means of the Feshbach resonance. We propose an explanation to the effect of the resonant splitting of the 2-soliton under the action of the NLM. Then, using systematic simulations and an analytical approach, we conclude that the weak quintic nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the self-defocusing quintic ...
Posted Content•
TL;DR: In this paper, the Cauchy problem for the cubic nonlinear Schroedinger equation, perturbed by higher order dissipative nonlinearities, is studied and global in-time existence of solutions for general initial data in the energy space is proved.
Abstract: We study the Cauchy problem for the cubic nonlinear Schroedinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions.
Journal Article•
TL;DR: In this paper, the collocation method using quintic B-spline is derived for solving the complex modified Korteweg-de Vries (CMKdV) problem.
TL;DR: In this article, the authors consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schr\"{o}dinger equation (NLSE), which includes a small quintic term, and weak resonant nonlinearity management (NLM).
Abstract: We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schr\"{o}dinger equation (NLSE), which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagation in media with cubic-quintic optical nonlinearities and periodic alternation of linear loss and gain, and to BEC, with the self-focusing quintic term accounting for the weak deviation of the dynamics from one-dimensionality, while the NLM can be induced by means of the Feshbach resonance. We propose an explanation to the effect of the resonant splitting of the 2-soliton under the action of the NLM. Then, using systematic simulations and an analytical approach, we conclude that the weak quintic nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the self-defocusing quintic nonlinearity accelerates its splitting. It is also shown that the quintic term with the self-defocusing/focusing sign makes the resonant response of the 2-soliton to the NLM essentially broader, in terms of the frequency.
TL;DR: In this article, the authors construct explicit solutions of quintic nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities using Lie group theory and canonical transformations and present the general theory and use it to study some examples.
Abstract: In this paper, using Lie group theory and canonical transformations, we construct explicit solutions of quintic nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory and use it to study some examples.
Posted Content•
05 Mar 2009
TL;DR: In this article, the generalized Hyers-Ulam-Rassias stability of a generalized mixed type of quartic, cubic, quadratic and additive functional equations in quasi-Banach spaces was obtained.
Abstract: On the Hyers–Ulam–Rassias stability of a generalized mixed type of quartic, cubic, quadratic and additive functional equations in quasi-Banach spaces Abstract. In this paper, we obtain the general solution and the generalized Hyers–Ulam– Rassias stability of the following functional equation in quasi-Banach spaces f (x + ky) + f (x − ky) = k 2 f (x + y) + k 2 f (x − y) + 2(1 − k 2)f (x) + k 2 (k 2 − 1) 12 (˜ f (2y) − 4 ˜ f (y)) for fixed integers k with k = 0, ±1 where˜f (y) := f (y) + f (−y). The results achieved in this paper are comprehensive such that contain the results in papers obtained by I. [21] and also some other papers.
01 Jan 2009
TL;DR: In this paper, the authors constructed an infinite family of curves with an AP of length 12 points in the form y 2 = f (x) where f(x) ∈ Q[x).
Abstract: Consider a degree five curve of the form y 2 = f(x) where f(x) ∈ Q[x]. Ulas previously showed the existence of an infinite family of curves C which contain an arithmetic progression (AP) of length 11. The author also found an example of said curve which contains 12 points in AP. In this paper, we construct an infinite family of curves with an AP of length 12.
TL;DR: In this paper, the quintic cyclic polynomials discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori were established.
Abstract: We establish an isomorphism between the quintic cyclic polynomials discovered by Hashimoto–Tsunogai and those arising from Kummer theory for certain algebraic tori This enables us to solve the isomorphism problem for Hashimoto–Tsunogai polynomials and also Brumer's quintic polynomials