Results 21 to 30 of about 37,190 (197)
Exact solutions to the focusing nonlinear Schrodinger equation [PDF]
, 2007 A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form
Ablowitz M J +28 more
core +5 more sources
Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions [PDF]
Cubo (Temuco), 2019 Summary: The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on \(\text{exp}(- x {}^2)\), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp.
Bagul, Yogesh J., Chesneau, Christophe
openaire +2 more sources
Expansion in the distance parameter for two vortices close together [PDF]
, 2000 Static vortices close together are studied for two different models in 2-dimen- sional Euclidean space. In a simple model for one complex field an expansion in the parameters describing the relative position of two vortices can be given in terms of ...
Bogomolnyi E. B. +5 more
core +3 more sources
A Systematic Approach to Delay Functions
Mathematics, 2023 We present a systematic introduction to a class of functions that provide fundamental solutions for autonomous linear integer-order and fractional-order delay differential equations.
Christopher N. Angstmann +4 more
doaj +1 more source
Advances in Difference Equations, 2018 In this paper, we aim to investigate q-analogues of the natural transform on various elementary functions of special type. We obtain results associated with classes of q-convolution products, Heaviside functions, q-exponential functions, q-hyperbolic ...
Shrideh K Al-Omari
doaj +1 more source
Computing hypergeometric functions rigorously [PDF]
, 2016 We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex parameters and ...
Johansson, Fredrik
core +5 more sources
Analytical Approximant to a Quadratically Damped Forced Cubic-Quintic Duffing Oscillator
The Scientific World Journal, 2022 The cubic-quintic Duffing oscillator of a system with strong quadratic damping and forcing is considered. We give elementary approximate analytical solution to this oscillator in terms of exponential and trigonometric functions. We compare the analytical
Alvaro H. S. Salas
doaj +1 more source
Classes of new analytical soliton solutions to some nonlinear evolution equations
Results in Physics, 2021 Undoubtedly, all applied sciences are closely corresponding to differential equations, especially partial differential equations. This contribution aims to examine the efficiency of a modified version of the generalized exponential rational function ...
Yan Cao +7 more
doaj +1 more source
Approximating trigonometric functions by using exponential inequalities
Journal of Inequalities and Applications, 2019 In this paper, some exponential inequalities are derived from the inequalities containing trigonometric functions. Numerical examples show that one can achieve much tighter bounds than those of prevailing methods, which are presented by Cusa, Huygens ...
Xiao-Diao Chen, Junyi Ma, Yixin Li
doaj +1 more source
Generalization of Caputo-Fabrizio Fractional Derivative and Applications to Electrical Circuits
Frontiers in Physics, 2020 A new fractional derivative with a non-singular kernel involving exponential and trigonometric functions is proposed in this paper. The suggested fractional operator includes as a special case Caputo-Fabrizio fractional derivative.
Amal Alshabanat +3 more
doaj +1 more source