Search · four archives
Search · four archives
18 papers · ranked by Valyu relevance
Dario Izzo, Francesco Biscani
Weierstrass elliptic and related functions have been recently shown to enable analytical explicit solutions to classical problems in astrodynamics. These include the constant radial acceleration problem, the Stark problem and the two-fixed center (or Euler's) problem. In this paper we review the basic technique that…
Raymond O. Wells
| 1 | Introduction | 1 | | --- | --- | --- | | 2 | The Complex Plane | 4 | | 3 | Abel's Theorem | 10 | | 4 | Elliptic Functions | 21 | | 5 | Holomorphic functions and mappings | 33 | | 6 | Riemann surfaces | 54 | | 7 | Conclusion | 69 |
Efe Gürel
In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions ζλ, zeta differences of first kind ∆λ and second kind ∆λ,µ where λ, µ = 1, 2, 3. Fundamental and novel results pertaining to these functions are proven. Furthermore, results already existing in the…
E. Yu. Bunkova
The interest in elliptic functions of level n is related to the fact that such functions determine elliptic Hirzebruch genera of level N, where n | N (see [3, 4]). In particular, the function f2(x) is the elliptic sine and determines the famous Oshanine–Witten elliptic genus [5]. In this work we propose an approach to…
Jean-Christophe Feauveau
Since Abel, Jacobi and Weiertsrass, the bases of the theory of the elliptic functions have been well established. Abel proceeds by a length inversion of arc of ellipse (which justifies the denomination of these functions), Jacobi introduces theta functions to define the elliptic functions, finally Weierstrass defines…
P. L. Robinson
The elliptic functions Let 0 (2-1) u=\int_{0}^{\phi}F({\frac{1}{4}},{\frac{3}{4}};{\frac{1}{2}};\kappa^{2}\sin^{2}\theta)\,\mathrm{d}\theta=\int_{0}^{\sin\phi}F({\frac{1}{4}},{\frac{3}{4}};{\frac{1}{2}};\kappa^{2}t^{2}){\frac{\mathrm{d}t}{\sqrt{1-t^{2}}}}. Near the origin, the relation φ ↦ u(φ) inverts to u ↦ φ(u) with…
Jian-ming Qi, Fu Zhang, Wen-jun Yuan, Zi-feng Huang
We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave…
Akhtar Hussain, Tarek F. Ibrahim, F. M. Osman Birkea, Abeer M. Alotaibi + 2 more
'Abeer M. Alotaibi' 'Bushra R. Al-Sinan' 'Herbert Mukalazi'] Despite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. The efficacy of this…
Hiroki Aoki, Kyoji Saito
Second, Eisenstein series of types B2 and G2, for the case when their weights are equal or greater than 3, are described by shifted classical Eisenstein series [Sa, §8]. Their holomorphicity at cusps and the values at cusps can be shown and calculated similar to the classical Eisenstein series by helps of Riemann's…
Mina M. Fahim, Hamdy M. Ahmed, K. A. Dib, Islam Samir
In this work, a sixth-order extension of the nonlinear Schrödinger equation (NLSE) within its integrable hierarchy is investigated to model higher-order nonlinear and dispersive effects relevant to optical fiber systems and nonlinear wave propagation. By employing the Improved Modified Extended Tanh Function Method, a…
Shun Adachi
In a previous study, the authors utilized a single dimensional operationalization of species density that at least partially demonstrated dynamic system behavior. For completeness, a theory needs to be developed related to homology/cohomology, induction of the time dimension, and system hierarchies. The topological…
B. C. Carlson
Three improvements in reduction and computation of elliptic integrals are made. 1. Reduction formulas, used to express many elliptic integrals in terms of a few standard integrals, are simplified by modifying the definition of intermediate “basic integrals.” 2. A faster than quadratically convergent series is given for…
Michael J. Schlosser, Meesue Yoo, Vitaly Kocharovsky
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a…
Ti-Ren Huang, Shen-Yang Tan, Xiao-Yan Ma, Yu-Ming Chu
We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
Mohammed F. Shehab, Hamdy M. Ahmed, Hisham H. Hussein
In this study, we investigate the stochastic nonlinear Schrödinger equation incorporating self-phase modulation under the influence of multiplicative white noise in the dispersionless regime. By employing the improved modified extended tanh function method , we derive a rich spectrum of analytical solutions, including…
Arturo Tozzi, James F. Peters, Norbert Jaušovec
The modular function j, central in the assessment of abstract mathematical problems, describes elliptic, intertwined trajectories that move in the planes of both real and complex numbers. Recent clues suggest that the j-function might display a physical counterpart, equipped with a quantifiable real component and a…
Amelia Carolina Sparavigna
In an article by Thibault et al., 2002, we can find measurements of Raman linewidths in the Q branch of carbon monoxide, for mixtures with Argon at different temperatures. A plot is available for the Q(5) line with a fitted Voigt function. Here we show that a q-Gaussian Tsallis function can be used for fitting this…
Authors not listed
In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of power law fluids in tubes of elliptical cross sections. We derive…