Results 11 to 20 of about 86,558 (263)

Classification of cubic equations

Lietuvos Matematikos Rinkinys, 2018
Rather unexpectably all real equations of the fourth degree are solvable by real means. So we can classify all real equations of the third and fourth degree. In this article we classify real cubics. The real quartics will be classified in another article.
Juvencijus Mačys, Jurgis Sušinskas
doaj   +1 more source

Peculiarities of Housing and Communal Services and the Difficulties of Implementing Energy-Saving Technologies: The Case of Kazakhstan

Energies, 2022
The article considers the problems arising in the implementation of energy-saving technologies in the housing and communal services sector of Kazakhstan, including the example of specific situations.
Anna Shevyakova, Yelena Petrenko, Gaukhar Koshebayeva, Dmitry Ulybyshev   +3 more
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Rational solutions of Painlevé systems. [PDF]

, 2019
arXiv admin note: substantial text overlap with arXiv:1811.09274, arXiv:1912 ...
Gomez-Ullate, David, Grandati, Yves, Milson, Robert   +2 more
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Multi-Parametric Families of Solutions of Order $N$ to the Boussinesq and KP Equations and the Degenerate Rational Case

Universal Journal of Mathematics and Applications, 2020
From elementary exponential functions which depend on several parameters, we construct multi-parametric solutions to the Boussinesq equation. When we perform a passage to the limit when one of these para\-meters goes to $0$, we get rational solutions as ...
Pierre Gaillard
doaj   +1 more source

Rational solutions of Riccati differential equation with coefficients rational [PDF]

Applied Mathematics and Computation, 2011
This paper presents a simple and efficient method for determining the rational solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation , is reducible, we look for the rational solutions of Riccati differential equation , by reducing the number of checks to be made and by
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Equations of higher orders

Lietuvos Matematikos Rinkinys, 2019
A complicated system of two equations with two variables is considered. The theory of equations of higher orders required for solution is given. Many different methods of solution are indicated.
Juozas Juvencijus Mačys
doaj   +1 more source

Explicit solutions of rational integrable differential-difference equations

Partial Differential Equations in Applied Mathematics, 2022
The rational integrable differential-difference equations are proposed from a different discrete spectral problem. We proved the Liouville integrability of rational integrable differential-difference equations by deriving its bi-Hamiltonian structures ...
Qiulan Zhao, Muhammad Arham Amin
doaj   +1 more source

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation

Mathematics, 2016
In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs) describing microtubules, by implementing the exp(−Φ(ξ))-Expansion Method ...
Nur Alam, Fethi Bin Muhammad Belgacem
doaj   +1 more source

Rational and semi-rational solutions to the Davey–Stewartson III equation

Nonlinear Dynamics, 2022
Abstract In this paper, based on the combination of Hirota’s bilinear method and long wave limit technique, we investigate rational and semi-rational solutions to the third-type Davey-Stewartson (DS III) equation and its nonlocal version. Rational solutions to the DS III equation demonstrate to be kinks, lumps and line rogue waves, while semi ...
Shengnan Wang, Guo-Fu Yu
openaire   +1 more source

Elementary theory of cubics and quartics

Lietuvos Matematikos Rinkinys, 2017
It is proved that cubic and quartic equations in real numbers can be solved elementarily, avoiding complex numbers and derivatives. Corresponding algorithms are presented.
Juozas Juvencijus Mačys
doaj   +1 more source