Wyniki wyszukiwania - BazTech

1

Comparison of main geometric characteristics of deformed sphere and standard spheroid

Kovalchuk Vasyl, Mladenov Ivaïlo M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2023

|

Vol. 71, nr 5

art. no. e147058

EN

In the paper we compare the geometric descriptions of the deformed sphere (i.e., the so-called λ-sphere) and the standard spheroid (namely, World Geodetic System 1984’s reference ellipsoid of revolution). Among the main geometric characteristics of those two surfaces of revolution embedded into the three-dimensional Euclidean space we consider the semi-major (equatorial) and semi-minor (polar) axes, quartermeridian length, surface area, volume, sphericity index, and tipping (bifurcation) point for geodesics. Next, the RMS (Root Mean Square) error is defined as the square-rooted arithmetic mean of the squared relative errors for the individual pairs of the discussed six main geometric characteristics. As a result of the process of minimization of the RMS error, we have obtained the proposition of the optimized value of the deformation parameter of the λ-sphere, for which we have calculated the absolute and relative errors for the individual pairs of the discussed main geometric characteristics of λ-sphere and standard spheroid (the relative errors are of the order of 10−6 – 10−9). Among others, it turns out that the value of the,sup> flattening factor of the spheroid is quite a good approximation for the corresponding value of the deformation parameter of the λ-sphere (the relative error is of the order of 10−4).

2

Meromorphic solutions of the(2+1)- and the (3+1)-dimensional BLMP equations and the (2+1)-dimensional KMN equation

Dang Guoqiang

Demonstratio Mathematica

|

2021

|

Vol. 54, nr 1

129--139

EN

The complex method is systematic and powerful to build various kinds of exact meromorphic solutions for nonlinear partial differential equations on the complex plane C. By using the complex method, abundant new exact meromorphic solutions to the (2 + 1)-dimensional and the (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equations and the (2 + 1)-dimension Kundu-Mukherjee-Naskar equation are investigated. Abundant new elliptic solutions, rational solutions and exponential solutions have been constructed.

3

On different kinds of solutions to simplified modified form of a Camassa-Holm equation

Gündoğdu Hami, Gözükızıl Ömer Faruk

Journal of Applied Mathematics and Computational Mechanics

|

2019

|

Vol. 18, nr 2

31--40

EN

In this research, our purpose is to investigate some types of solutions to a simplified modified form of the Camassa-Holm equation. The Jacobi elliptic function expansion method is applied to this equation. Then, a lot of travelling wave solutions are obtained. The derived solutions are in the form of Jacobi elliptic functions, hyperbolic functions, and trigonometric functions. Graphics of solutions are drawn in order to determine the types of the solutions. Furthermore, different kinds of solutions such as the singular kink wave solution, the kink wave solution, and the periodic solution are achieved.